Stuttgart 2004
2023
Julià Cufí, Agustí Reventós
A historical review of the Cauchy-Riemann equations and the Cauchy Theorem Journal Article
In: 2023.
@article{nokey,
title = {A historical review of the Cauchy-Riemann equations and the Cauchy Theorem},
author = {Julià Cufí, Agustí Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2023/11/cauchy2023octubre-ENGLISH.pdf},
year = {2023},
date = {2023-11-30},
urldate = {2023-11-30},
abstract = {Història de les equacions de Cauchy-Riemann},
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pubstate = {published},
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Història de les equacions de Cauchy-Riemann
J. Bruna, J. Cufí, E. Gallego, A. Reventós
On Crofton’s type formulas and the solid angle of convex sets Journal Article
In: Beiträge zur Algebra und Geometrie, 2023.
@article{nokey,
title = {On Crofton’s type formulas and the solid angle of convex sets},
author = {J. Bruna, J. Cufí, E. Gallego, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2024/04/Beitragen.pdf},
year = {2023},
date = {2023-03-23},
journal = {Beiträge zur Algebra und Geometrie},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2021
J. Cufí, E. Gallego; A, Reventós
Integral Geometry of pairs of planes Journal Article
In: Archiv der Mathematik, vol. 117, pp. 579-591, 2021.
@article{11,
title = {Integral Geometry of pairs of planes },
author = {J. Cufí, E. Gallego and A, Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/IntegralGeometryOfPairsOfPlaneARCHIV.pdf},
year = {2021},
date = {2021-01-01},
journal = {Archiv der Mathematik},
volume = {117},
pages = {579-591},
abstract = {We deal with integrals of invariant measures of pairs of planes in euclidean space as considered by Hug and Schneider. In this paper we express some of these integrals in terms of functions of the visual angle of a convex set.As a consequence of our results we evaluate the deficit in a Crofton-type inequality due to Blashcke.},
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We deal with integrals of invariant measures of pairs of planes in euclidean space as considered by Hug and Schneider. In this paper we express some of these integrals in terms of functions of the visual angle of a convex set.As a consequence of our results we evaluate the deficit in a Crofton-type inequality due to Blashcke.
2019
J. Cufí, E. Gallego; A. Reventós
Integral geometry about the visual angle of a convex set Journal Article
In: Rendiconti del Circolo Matematico di Palermo , vol. 69, pp. 1115-1120, 2019.
@article{10,
title = {Integral geometry about the visual angle of a convex set},
author = {J. Cufí, E. Gallego and A. Reventós
},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/Cufí2019_Article_IntegralGeometryAboutTheVisual.pdf},
year = {2019},
date = {2019-10-15},
journal = {Rendiconti del Circolo Matematico di Palermo },
volume = {69},
pages = {1115-1120},
abstract = {In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these formulas in terms of integrals of functions with respect to the canonical density in the space of pairs of lines and to give new simpler proofs of them.},
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pubstate = {published},
tppubtype = {article}
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In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these formulas in terms of integrals of functions with respect to the canonical density in the space of pairs of lines and to give new simpler proofs of them.
J. Cufí, E. Gallego; A. Reventós
On the integral formulas of Crofton and Hurwitz relative to the visual angle of a convex set Journal Article
In: Mathematika, vol. 65, pp. 874-896, 2019.
@article{13,
title = {On the integral formulas of Crofton and Hurwitz relative to the visual angle of a convex set},
author = {J. Cufí, E. Gallego and A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/CGR.pdf},
year = {2019},
date = {2019-06-01},
urldate = {2019-06-01},
journal = {Mathematika},
volume = {65},
pages = {874-896},
abstract = {We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santalo ́ for Masotti’s integral.},
keywords = {},
pubstate = {published},
tppubtype = {article}
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We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santalo ́ for Masotti’s integral.
J. Cufí, A. Reventós; C. J. Rodríguez
A discrete approach to Wirtinger inequality Journal Article
In: Journal of Mathematical Inequalities, vol. 13, no. 3, pp. 737-745, 2019.
@article{12,
title = {A discrete approach to Wirtinger inequality},
author = {J. Cufí, A. Reventós and C. J. Rodríguez},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/jmi-13-50.pdf},
year = {2019},
date = {2019-02-01},
journal = {Journal of Mathematical Inequalities},
volume = {13},
number = {3},
pages = {737-745},
abstract = {Considering Wirtinger’s inequality for piece-wise equipartite functions we find a dis- crete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger’s inequality that also allows to study the case of equality. Moreover it leads in a natural way to the Fourier series development of 2π -periodic functions.},
keywords = {},
pubstate = {published},
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}
Considering Wirtinger’s inequality for piece-wise equipartite functions we find a dis- crete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger’s inequality that also allows to study the case of equality. Moreover it leads in a natural way to the Fourier series development of 2π -periodic functions.
2018
J. Cufí, E. Gallego; A. Reventós
A note on Hurwitz’s inequality Journal Article
In: Journal of Mathematical Analysis and Applications, vol. 458, pp. 436-451, 2018.
@article{1k,
title = {A note on Hurwitz’s inequality},
author = {J. Cufí, E. Gallego and A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2018/10/JMAA.pdf},
year = {2018},
date = {2018-10-01},
journal = {Journal of Mathematical Analysis and Applications},
volume = {458},
pages = {436-451},
abstract = {Given a simple closed plane curve Γ of length L enclosing a compact convex set
K of area F, Hurwitz found an upper bound for the isoperimetric deficit, namely
L2 − 4πF ≤ π|Fe|, where Fe is the algebraic area enclosed by the evolute of Γ. In
this note we improve this inequality finding strictly positive lower bounds for the
deficit π|Fe|−Δ, where Δ = L2 −4πF. These bounds involve either the visual angle
of Γ or the pedal curve associated to K with respect to the Steiner point of K or
the L2 distance between K and the Steiner disk of K. For compact convex sets of
constant width Hurwitz’s inequality can be improved to L2 −4πF ≤ 4 π|Fe|. In this 9
case we also get strictly positive lower bounds for the deficit 4 π|Fe| − Δ. For each 9
established inequality we study when equality holds. This occurs for those compact convex sets being bounded by a curve parallel to an hypocycloid of 3, 4 or 5 cusps or the Minkowski sum of this kind of sets.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Given a simple closed plane curve Γ of length L enclosing a compact convex set
K of area F, Hurwitz found an upper bound for the isoperimetric deficit, namely
L2 − 4πF ≤ π|Fe|, where Fe is the algebraic area enclosed by the evolute of Γ. In
this note we improve this inequality finding strictly positive lower bounds for the
deficit π|Fe|−Δ, where Δ = L2 −4πF. These bounds involve either the visual angle
of Γ or the pedal curve associated to K with respect to the Steiner point of K or
the L2 distance between K and the Steiner disk of K. For compact convex sets of
constant width Hurwitz’s inequality can be improved to L2 −4πF ≤ 4 π|Fe|. In this 9
case we also get strictly positive lower bounds for the deficit 4 π|Fe| − Δ. For each 9
established inequality we study when equality holds. This occurs for those compact convex sets being bounded by a curve parallel to an hypocycloid of 3, 4 or 5 cusps or the Minkowski sum of this kind of sets.
K of area F, Hurwitz found an upper bound for the isoperimetric deficit, namely
L2 − 4πF ≤ π|Fe|, where Fe is the algebraic area enclosed by the evolute of Γ. In
this note we improve this inequality finding strictly positive lower bounds for the
deficit π|Fe|−Δ, where Δ = L2 −4πF. These bounds involve either the visual angle
of Γ or the pedal curve associated to K with respect to the Steiner point of K or
the L2 distance between K and the Steiner disk of K. For compact convex sets of
constant width Hurwitz’s inequality can be improved to L2 −4πF ≤ 4 π|Fe|. In this 9
case we also get strictly positive lower bounds for the deficit 4 π|Fe| − Δ. For each 9
established inequality we study when equality holds. This occurs for those compact convex sets being bounded by a curve parallel to an hypocycloid of 3, 4 or 5 cusps or the Minkowski sum of this kind of sets.
2016
J. Cufí, A. Reventós
A lower bound for the isoperimetric deficit Journal Article
In: Elemente der Mathematik, vol. 71, pp. 156-167, 2016.
@article{1i,
title = { A lower bound for the isoperimetric deficit},
author = {J. Cufí, A. Reventós },
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2018/10/Cufi-Reventos.pdf},
year = {2016},
date = {2016-10-01},
journal = {Elemente der Mathematik},
volume = {71},
pages = {156-167},
abstract = {Fu ̈r jede Figur K in der Ebene mit Umfang L und Fla ̈che F gilt die isoperimetrische Ungleichung := L 2 − 4π F ≥ 0. Gleichheit gilt genau fu ̈ r Kreise. Hurwitz gelang 1902 nicht nur ein eleganter Beweis der isoperimetrischen Ungleichung mit Hilfe von Fourier-Reihen, er bewies zudem eine obere Schranke fu ̈r das isoperimetrische Defizit , indem er die Evolute der Kurve ins Spiel brachte. 1920 fand Bonnesen eine un- tere Schranke fu ̈r , na ̈mtlich π(R − r)2 ≤ , wobei R und r den Um- respektive den Inkreisradius der Randkurve C der betrachteten Figur K bezeichnen. In der vor- liegenden Arbeit wird eine andere untere Schranke fu ̈r bewiesen: Diese ergibt sich aus der Differenz der von C umrandeten Fla ̈che und der Fla ̈che welche die Pedalkurve von C bezu ̈glich des Steiner-Punktes von C einschliesst. Das Resultat verbessert damit Abscha ̈tzungen z.B. von Groemer. Es wird zudem bestimmt, fu ̈r welche Kurven die neue Abscha ̈tzung scharf ist.},
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Fu ̈r jede Figur K in der Ebene mit Umfang L und Fla ̈che F gilt die isoperimetrische Ungleichung := L 2 − 4π F ≥ 0. Gleichheit gilt genau fu ̈ r Kreise. Hurwitz gelang 1902 nicht nur ein eleganter Beweis der isoperimetrischen Ungleichung mit Hilfe von Fourier-Reihen, er bewies zudem eine obere Schranke fu ̈r das isoperimetrische Defizit , indem er die Evolute der Kurve ins Spiel brachte. 1920 fand Bonnesen eine un- tere Schranke fu ̈r , na ̈mtlich π(R − r)2 ≤ , wobei R und r den Um- respektive den Inkreisradius der Randkurve C der betrachteten Figur K bezeichnen. In der vor- liegenden Arbeit wird eine andere untere Schranke fu ̈r bewiesen: Diese ergibt sich aus der Differenz der von C umrandeten Fla ̈che und der Fla ̈che welche die Pedalkurve von C bezu ̈glich des Steiner-Punktes von C einschliesst. Das Resultat verbessert damit Abscha ̈tzungen z.B. von Groemer. Es wird zudem bestimmt, fu ̈r welche Kurven die neue Abscha ̈tzung scharf ist.
B. Herrera, J.Pallarés; A. Reventós
Geometric characterization of the rotation centers of a particle in a flow Journal Article
In: Note di Matematica, vol. 36, pp. 37-47, 2016.
@article{14,
title = {Geometric characterization of the rotation centers of a particle in a flow},
author = {B. Herrera, J.Pallarés and A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/NOTEMAT_VOL_36_2-2-2.pdf},
year = {2016},
date = {2016-01-10},
urldate = {2016-01-10},
journal = {Note di Matematica},
volume = {36},
pages = {37-47},
abstract = {We provide a geometrical characterization of the instantaneous rotation centers
O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific
instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best
fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical
locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We provide a geometrical characterization of the instantaneous rotation centers
O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific
instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best
fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical
locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).
O (p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific
instant t, the point O (p, t) is the center of curvature at the vertex of the parabola which best
fits the path-particle line γ (t) on its Darboux plane at p, and b) over time t, the geometrical
locus of O (p, t) is the line of striction of the principal normal surface generated by γ (t).
2015
J. Cufí, A. Reventós; C. Rodríguez
Curvature for Polygons Journal Article
In: The American Mathematical Monthly, vol. 122, pp. 332-337, 2015.
@article{1j,
title = {Curvature for Polygons},
author = {J. Cufí, A. Reventós and C. Rodríguez},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2018/10/amer.math_.monthly.122.04.332.pdf},
year = {2015},
date = {2015-10-01},
journal = {The American Mathematical Monthly},
volume = {122},
pages = {332-337},
abstract = {Using a notion of curvature at the vertices of a polygon, we prove an inequality involving the length of the sides of the polygon and the radii of curvature at the vertices. As a consequence, we obtain a discrete version of Ros’ inequality.},
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tppubtype = {article}
}
Using a notion of curvature at the vertices of a polygon, we prove an inequality involving the length of the sides of the polygon and the radii of curvature at the vertices. As a consequence, we obtain a discrete version of Ros’ inequality.
2014
J. Cufí, A. Reventós
EVOLUTES AND ISOPERIMETRIC DEFICIT IN TWO-DIMENSIONAL SPACES OF CONSTANT CURVATURE Journal Article
In: ARCHIVUM MATHEMATICUM (BRNO), vol. 50, pp. 219-236, 2014.
@article{1h,
title = {EVOLUTES AND ISOPERIMETRIC DEFICIT IN TWO-DIMENSIONAL SPACES OF CONSTANT CURVATURE},
author = {J. Cufí, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2018/10/Versio-archivum.pdf},
year = {2014},
date = {2014-10-01},
journal = {ARCHIVUM MATHEMATICUM (BRNO)},
volume = {50},
pages = {219-236},
abstract = {We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.
2012
J. Abardia, C. J. Rodríguez; A. Reventós
What did Gauss read in the Appendix? Journal Article
In: Historia Mathematika, vol. 39, pp. 292-323, 2012.
@article{15,
title = {What did Gauss read in the Appendix?},
author = {J. Abardia, C. J. Rodríguez and A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/YHMAT2784.pdf},
year = {2012},
date = {2012-05-04},
urldate = {2012-05-04},
journal = {Historia Mathematika},
volume = {39},
pages = {292-323},
abstract = {In a clear analogy with spherical geometry, Lambert states that in an “imaginary sphere” the sum of the angles of a triangle would be less than p. In this paper we analyze the role played by this imaginary sphere in the development of non-Euclidean geometry, and how it served Gauss as a guide. More precisely, we analyze Gauss’s reading of Bolyai’s Appendix in 1832, five years after the publication of Disquisitiones generales circa superficies curvas, on the assumption that his investigations into the foundations of geometry were aimed at finding, among the surfaces in space, Lambert’s hypothetical imaginary sphere. We also wish to show that the close relation between differential geometry and non-Euclidean geometry is already present in János Bol- yai’s Appendix, that is, well before its appearance in Beltrami’s Saggio. From this point of view, one is able to answer certain natural questions about the history of non-Euclidean geometry; for instance, why Gauss decided not to write further on the subject after reading the Appendix.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In a clear analogy with spherical geometry, Lambert states that in an “imaginary sphere” the sum of the angles of a triangle would be less than p. In this paper we analyze the role played by this imaginary sphere in the development of non-Euclidean geometry, and how it served Gauss as a guide. More precisely, we analyze Gauss’s reading of Bolyai’s Appendix in 1832, five years after the publication of Disquisitiones generales circa superficies curvas, on the assumption that his investigations into the foundations of geometry were aimed at finding, among the surfaces in space, Lambert’s hypothetical imaginary sphere. We also wish to show that the close relation between differential geometry and non-Euclidean geometry is already present in János Bol- yai’s Appendix, that is, well before its appearance in Beltrami’s Saggio. From this point of view, one is able to answer certain natural questions about the history of non-Euclidean geometry; for instance, why Gauss decided not to write further on the subject after reading the Appendix.
2010
E. Gallego, A. Reventós, G. Solanes; E. Teufel
A kinematic formula for the total absolute curvature of intersections Journal Article
In: Advances in Geometry, vol. 10, pp. 709-718, 2010.
@article{nokey,
title = {A kinematic formula for the total absolute curvature of intersections},
author = {E. Gallego, A. Reventós, G. Solanes and E. Teufel},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/KinematicAdvancesGeometry.pdf},
year = {2010},
date = {2010-06-30},
urldate = {2010-06-30},
journal = {Advances in Geometry},
volume = {10},
pages = {709-718},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2009
E. Gallego, A. Reventós, G. Solanes, E. Teufel
Horospheres in Hyperbolic Geometry Journal Article
In: Centre Recerca Matemàtica, no. 805, pp. 1-20, 2009.
@article{16,
title = {Horospheres in Hyperbolic Geometry},
author = {E. Gallego, A. Reventós, G. Solanes, E. Teufel},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/CRM_prep_envelopesTEDI.pdf},
year = {2009},
date = {2009-06-01},
urldate = {2009-06-01},
journal = {Centre Recerca Matemàtica},
number = {805},
pages = {1-20},
abstract = {In this paper we investigate the role of horo- spheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combination” of support maps or curves. Finally we ob- tain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper we investigate the role of horo- spheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combination” of support maps or curves. Finally we ob- tain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.
2008
E. Gallego, A. Reventós, G. Solanes, E. Teufel
Width of convex bodies in spaces of constant curvature Journal Article
In: Manuscripta Mathematica, vol. 126, pp. 115-134, 2008.
@article{nokey,
title = {Width of convex bodies in spaces of constant curvature},
author = {E. Gallego, A. Reventós, G. Solanes, E. Teufel},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/VersioManuscripta.pdf},
year = {2008},
date = {2008-01-10},
urldate = {2008-01-10},
journal = {Manuscripta Mathematica},
volume = {126},
pages = {115-134},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2007
C. A. Escudero, A. Reventós, G. Solanes
Focal sets in two-dimensional space forms Journal Article
In: Pacific Journal of Mathematics, vol. 233, no. 2, pp. 309-320, 2007.
@article{16c,
title = {Focal sets in two-dimensional space forms},
author = {C. A. Escudero, A. Reventós, G. Solanes},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/versiopublicada.pdf},
year = {2007},
date = {2007-12-11},
urldate = {2007-12-11},
journal = {Pacific Journal of Mathematics},
volume = {233},
number = {2},
pages = {309-320},
abstract = {We relate the area of a convex set in a 2-dimensional space of constant curvature with some integrals over the curvature radius at its boundary.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We relate the area of a convex set in a 2-dimensional space of constant curvature with some integrals over the curvature radius at its boundary.
C. A. Escudero, A. Reventós
An interesting property of the evolute Journal Article
In: The American Mathematical Monthly , vol. 114, no. 7, pp. 623-628, 2007.
@article{18,
title = {An interesting property of the evolute},
author = {C. A. Escudero, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/monthly623-628-escudero.pdf},
year = {2007},
date = {2007-07-11},
urldate = {2007-07-11},
journal = {The American Mathematical Monthly },
volume = {114},
number = {7},
pages = {623-628},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2006
C. A. Escudero, A. Reventós, G. Solanes
An interesting property of the evolute Journal Article
In: ICM 2006, 2006.
@article{nokey,
title = {An interesting property of the evolute},
author = {C. A. Escudero, A. Reventós, G. Solanes},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/poster2.pdf},
year = {2006},
date = {2006-06-04},
urldate = {2006-06-04},
journal = {ICM 2006},
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pubstate = {published},
tppubtype = {article}
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2001
A.A. Borisenko, E.Gallego, A.Reventós
Relation between area and volume for λ-convex sets in Hadamard manifolds Journal Article
In: Differential Geometry and its Applications, vol. 14, pp. 267-280, 2001.
@article{19,
title = {Relation between area and volume for λ-convex sets in Hadamard manifolds},
author = {A.A. Borisenko, E.Gallego, A.Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/BGR.pdf},
year = {2001},
date = {2001-06-01},
urldate = {2001-06-01},
journal = {Differential Geometry and its Applications},
volume = {14},
pages = {267-280},
abstract = {It is known that for a sequence {t } of convex sets expanding over the whole hyperbolic space Hn+1 the limit of the quotient vol(t )/vol(∂t ) is less or equal than 1/n, and exactly 1/n when the sets considered are convex with respect to horocycles. When convexity is with respect to equidistant lines, i.e., curves with constant geodesic curvature λ less than one, the above limit has λ/n as lower bound. Looking how the boundary bends, in this paper we give bounds of the above quotient for a compact λ-convex domain in a complete simply-connected manifold of negative and bounded sectional curvature, a Hadamard manifold. Then we see that the limit of vol(t )/vol(∂ t ) for sequences of λ-convex domains expanding over the whole space lies between the values λ/nk2 and 1/nk .},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
It is known that for a sequence {t } of convex sets expanding over the whole hyperbolic space Hn+1 the limit of the quotient vol(t )/vol(∂t ) is less or equal than 1/n, and exactly 1/n when the sets considered are convex with respect to horocycles. When convexity is with respect to equidistant lines, i.e., curves with constant geodesic curvature λ less than one, the above limit has λ/n as lower bound. Looking how the boundary bends, in this paper we give bounds of the above quotient for a compact λ-convex domain in a complete simply-connected manifold of negative and bounded sectional curvature, a Hadamard manifold. Then we see that the limit of vol(t )/vol(∂ t ) for sequences of λ-convex domains expanding over the whole space lies between the values λ/nk2 and 1/nk .
1999
Eduard Gallego, Agustí Reventós
Asymptotic Behaviour of λ-Convex Sets in the Hyperbolic Plane Journal Article
In: Geometriae Dedicata, vol. 76, pp. 275-289, 1999.
@article{1d,
title = {Asymptotic Behaviour of λ-Convex Sets in the Hyperbolic Plane},
author = {Eduard Gallego, Agustí Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2018/10/GeometriaeDedicata.pdf},
year = {1999},
date = {1999-01-01},
journal = {Geometriae Dedicata},
volume = {76},
pages = {275-289},
abstract = {It is known that the limit Area/Length for a sequence of convex sets expanding over the whole hyperbolic plane is less than or equal to 1, and exactly 1 when the sets considered are convex with respect to horocycles. We consider geodesics and horocycles as particular cases of curves of constant geodesic curvature λ with 0 < λ < 1 and we study the above limit Area/Length as a function of the parameter λ.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
It is known that the limit Area/Length for a sequence of convex sets expanding over the whole hyperbolic plane is less than or equal to 1, and exactly 1 when the sets considered are convex with respect to horocycles. We consider geodesics and horocycles as particular cases of curves of constant geodesic curvature λ with 0 < λ < 1 and we study the above limit Area/Length as a function of the parameter λ.
1997
B. Herrera, A. Reventós
The transverse structure of Lie flows of codimension 3 Journal Article
In: J. Math. Kyoto Univ., vol. 37, no. 3, pp. 455-476, 1997.
@article{20,
title = { The transverse structure of Lie flows of codimension 3},
author = {B. Herrera, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/Kyoto-1997-vol-37.pdf},
year = {1997},
date = {1997-06-11},
urldate = {1997-06-11},
journal = {J. Math. Kyoto Univ.},
volume = {37},
number = {3},
pages = {455-476},
abstract = {This paper deals with the problem of the realization of a given Lie algebra as transverse algebra to a Lie foliation on a compact manifold.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This paper deals with the problem of the realization of a given Lie algebra as transverse algebra to a Lie foliation on a compact manifold.
1996
B. Herrerra. M. Llabrés, A.Reventós
Transverse structure of Lie foliations Journal Article
In: J. Math. Soc. Japan, vol. 48, no. 4, pp. 769-795, 1996.
@article{21,
title = {Transverse structure of Lie foliations},
author = {B. Herrerra. M. Llabrés, A.Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/J.Soc_.Math-Japan.pdf},
year = {1996},
date = {1996-06-11},
urldate = {1996-06-11},
journal = {J. Math. Soc. Japan},
volume = {48},
number = {4},
pages = {769-795},
abstract = {This paper deals with the problem of the realization of a given Lie algebra as transverse algebra to a Lie foliation on a compact manifold.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This paper deals with the problem of the realization of a given Lie algebra as transverse algebra to a Lie foliation on a compact manifold.
1991
E. Gallego, A. Reventós
Lie flows of codimension 3 Journal Article
In: Transactions of the American Mathematical Society, vol. 326, no. 2, pp. 529-541, 1991.
@article{23,
title = {Lie flows of codimension 3},
author = {E. Gallego, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/S0002-9947-1991-1005934-4.pdf},
year = {1991},
date = {1991-06-11},
urldate = {1991-06-11},
journal = {Transactions of the American Mathematical Society},
volume = {326},
number = {2},
pages = {529-541},
abstract = {Given a Lie algebra G of dmension 3 is there a compact manifold endowed with a Lie flowtranverely modeled on G ? },
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Given a Lie algebra G of dmension 3 is there a compact manifold endowed with a Lie flowtranverely modeled on G ?
1989
E . Gallego, L . Gualandri, G . Hector, A . Reventós
Groupoïdes Riemanniens Journal Article
In: Pub. Mat. UAB, vol. 33, pp. 417-422, 1989.
@article{nokey,
title = {Groupoïdes Riemanniens},
author = {E . Gallego, L . Gualandri, G . Hector, A . Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/37597-Text-de-larticle-37564-1-10-20060428.pdf},
year = {1989},
date = {1989-06-01},
urldate = {1989-06-01},
journal = {Pub. Mat. UAB},
volume = {33},
pages = {417-422},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
1988
M. Llabrés, A.Reventós
Unimodular Lie foliations Journal Article
In: Annales de la Faculté de Sciences de Toulouse, vol. 9, no. 2, pp. 243-255, 1988.
@article{22,
title = {Unimodular Lie foliations},
author = {M. Llabrés, A.Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/UnimodulatLieFoliations.pdf},
year = {1988},
date = {1988-05-11},
urldate = {1988-05-11},
journal = {Annales de la Faculté de Sciences de Toulouse},
volume = {9},
number = {2},
pages = {243-255},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Eduard Gallego, Agustí Reventós
Courbure et champs de plans Journal Article
In: C.R.A.S.P., vol. 306, pp. 675-679, 1988.
@article{Gallego1988,
title = {Courbure et champs de plans},
author = {Eduard Gallego, Agustí Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2018/10/crasp.pdf},
year = {1988},
date = {1988-01-01},
urldate = {1988-01-01},
journal = {C.R.A.S.P.},
volume = {306},
pages = {675-679},
abstract = {Soit M une variété riemanniene orientée munie de deux champs de plans F et H orientés, orthogonaux et complémentaires l’un de l’autre.
Suivant Albert ([1]) on obtient quelques formules intégrales donnant des relations entre la géométrie de la variété d’une part, et celle des champs de plans (courbure, intégrabilité et deuxième forme fondamentale), d’autre part.
On generalise un resultat de [3] a codimension arbitraire et sans hypothèse d’intégrabilit é.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Soit M une variété riemanniene orientée munie de deux champs de plans F et H orientés, orthogonaux et complémentaires l’un de l’autre.
Suivant Albert ([1]) on obtient quelques formules intégrales donnant des relations entre la géométrie de la variété d’une part, et celle des champs de plans (courbure, intégrabilité et deuxième forme fondamentale), d’autre part.
On generalise un resultat de [3] a codimension arbitraire et sans hypothèse d’intégrabilit é.
Suivant Albert ([1]) on obtient quelques formules intégrales donnant des relations entre la géométrie de la variété d’une part, et celle des champs de plans (courbure, intégrabilité et deuxième forme fondamentale), d’autre part.
On generalise un resultat de [3] a codimension arbitraire et sans hypothèse d’intégrabilit é.
1985
Eduard Gallego, Agustí Reventós
ASYMPTOTIC BEHAVIOR OF CONVEX SETS IN THE HYPERBOLIC PLANE Journal Article
In: Journal of Differential Geometry, vol. 21, pp. 63-72, 1985.
@article{Gallego1985,
title = {ASYMPTOTIC BEHAVIOR OF CONVEX SETS IN THE HYPERBOLIC PLANE},
author = {Eduard Gallego, Agustí Reventós},
url = {http://mat.uab.cat/web/agusti/jdg/},
year = {1985},
date = {1985-02-04},
journal = {Journal of Differential Geometry},
volume = {21},
pages = {63-72},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
1984
M. Nicolau, A. Reventós
On some geometrical properties of Seifert bundles Journal Article
In: Israel Journal of Mathematics, vol. 47, no. 4, pp. 323-334, 1984.
@article{24,
title = {On some geometrical properties of Seifert bundles},
author = {M. Nicolau, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/onsomegeometrical.pdf},
year = {1984},
date = {1984-06-11},
urldate = {1984-06-11},
journal = {Israel Journal of Mathematics},
volume = {47},
number = {4},
pages = {323-334},
abstract = {In this paper we use the integration along the leaves introduced by Haefliger in 1980to obtain a differentiable version of the Gysin sequence and Euler class for compact Hausdorff orientable foliations with generic leaf the sphere Sp. From this we give a geometrical significance to the vanishing of the Euler class on Seifert bundles. We also obtain an integral formula on Seifert bundles similar to
the Gauss-Bonnet one.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper we use the integration along the leaves introduced by Haefliger in 1980to obtain a differentiable version of the Gysin sequence and Euler class for compact Hausdorff orientable foliations with generic leaf the sphere Sp. From this we give a geometrical significance to the vanishing of the Euler class on Seifert bundles. We also obtain an integral formula on Seifert bundles similar to
the Gauss-Bonnet one.
the Gauss-Bonnet one.
1982
J. Llibre, A. Reventós
On the structure of the set of periodic points of a continuous map of the interval Journal Article
In: Archiv der Mathematik, vol. 39, pp. 331-334, 1982.
@article{nokey,
title = {On the structure of the set of periodic points of a continuous map of the interval},
author = {J. Llibre, A. Reventós },
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/cover.pdf},
year = {1982},
date = {1982-10-10},
urldate = {1982-10-10},
journal = {Archiv der Mathematik},
volume = {39},
pages = {331-334},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
J.Llibre, A. Reventós
Sur le nombre d’orbites periodiques d’une application du cercle en lui même. Journal Article
In: Comptes Rendues Acad. Scien. Paris, vol. 294, pp. 51-54, 1982.
@article{nokey,
title = {Sur le nombre d’orbites periodiques d’une application du cercle en lui même.},
author = {J.Llibre, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/Comptes_rendus_des_séances_de_...Académie_des_bpt6k5533029f-1.pdf},
year = {1982},
date = {1982-06-30},
urldate = {1982-06-30},
journal = {Comptes Rendues Acad. Scien. Paris},
volume = {294},
pages = {51-54},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A. Díaz MIranda, A. Reventós
Homogeneous contact compact manifolds and homogeneous symplectic manifolds Journal Article
In: Bulletin de la Société Mathématique de France , vol. 106, pp. 337-350, 1982.
@article{25,
title = {Homogeneous contact compact manifolds and homogeneous symplectic manifolds},
author = {A. Díaz MIranda, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/bulletinSciMath.pdf},
year = {1982},
date = {1982-06-11},
urldate = {1982-06-11},
journal = {Bulletin de la Société Mathématique de France },
volume = {106},
pages = {337-350},
abstract = {On montre que la fibration de Boothby et Wang donne une correspondance biejctive entre l'ensemble des variétés compactes homogénes de contact et célui des variétés compactes symplectiques.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
On montre que la fibration de Boothby et Wang donne une correspondance biejctive entre l'ensemble des variétés compactes homogénes de contact et célui des variétés compactes symplectiques.
J. Llibre, A. Reventós
On the number of fixed points for a continuous map of a finite connected graph Journal Article
In: Collectanea Mathematica, vol. 32, pp. 203-220, 1982.
@article{nokey,
title = {On the number of fixed points for a continuous map of a finite connected graph},
author = {J. Llibre, A. Reventós},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/COLLECTANEAMATHEMATICA_1981_32_03_02.pdf},
year = {1982},
date = {1982-05-11},
urldate = {1982-05-11},
journal = {Collectanea Mathematica},
volume = {32},
pages = {203-220},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
1980
J.Llibre, A. Reventós
Sobre el nombre de punts fixos per a una apliació d'un graf connex finit Journal Article
In: Pub. Mat. UAB, vol. 21, pp. 103-106, 1980.
@article{nokey,
title = {Sobre el nombre de punts fixos per a una apliació d'un graf connex finit},
author = {J.Llibre, A. Reventós },
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/puntsFixosGraf.pdf},
year = {1980},
date = {1980-10-10},
urldate = {1980-10-10},
journal = {Pub. Mat. UAB},
volume = {21},
pages = {103-106},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A. Díaz-Miranda, A. Reventós
Homogeneous compact contact manifolds aand homogeneous symplectic manifolds Journal Article
In: Pub. Mat. UAB, vol. 21, pp. 25-27, 1980.
@article{nokey,
title = { Homogeneous compact contact manifolds aand homogeneous symplectic manifolds},
author = {A. Díaz-Miranda, A. Reventós },
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2022/01/homogeneous.pdf},
year = {1980},
date = {1980-06-02},
urldate = {1980-06-02},
journal = {Pub. Mat. UAB},
volume = {21},
pages = {25-27},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
1979
A. Reventós
On the Gauss Bonnet formula on odd dimensional manifolds Journal Article
In: Tôhoku Mathematical Journal, vol. 31, pp. 165-178, 1979.
@article{26,
title = {On the Gauss Bonnet formula on odd dimensional manifolds},
author = {A. Reventós
},
url = {http://mat.uab.cat/web/agusti/wp-content/uploads/sites/13/2021/12/Tohoku.pdf},
year = {1979},
date = {1979-06-30},
urldate = {1979-06-30},
journal = {Tôhoku Mathematical Journal},
volume = {31},
pages = {165-178},
keywords = {},
pubstate = {published},
tppubtype = {article}
}