Gil Solanes

Professor Agregat (Serra Húnter Fellow)

Departament de Matemàtiques

Universitat Autònoma de Barcelona

and

Centre de Recerca Matemàtica

Address: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalunya, Spain.
Phone: +34 93 581 4537
E-mail: gil 'DOT' solanes 'AT' uab 'DOT' cat
Office: C1/112

Publications

  • Gil Solanes, Juan Andrés Trillo, Tube formulas for valuations in complex space forms, Math. Ann. 391 (2025), 881--913.
  • Florent Balacheff, Gil Solanes, Kroum Tzanev, Projective transformations of convex bodies and volume product, IMRN (2024), n.11, 9054--9065.
  • Andreas Bernig, Joseph H.G. Fu, Gil Solanes, Thomas Wannerer, The Weyl tube theorem for Kähler manifolds, arXiv:2209.05806
  • Andreas Bernig, Dmitry Faifman, Gil Solanes, Crofton formulas in pseudo-Riemannian space forms, Compositio Math. 158 (2022), no. 10, 1935--1979.
  • Andreas Bernig, Dmitry Faifman, Gil Solanes, Curvature Measures of Pseudo-Riemannian Manifolds, J. Reine Angew. Math. 788 (2022), 77--127
  • Florent Balacheff, Gil Solanes, Kroum Tzanev, The Santaló point for the Holmes-Thompson boundary area, Adv. Math. 397 (2022).
  • Andreas Bernig, Dmitry Faifman, Gil Solanes, Uniqueness of curvature measures in pseudo-Riemannian geometry, Journal of Geometric Analysis 31 (2021), 11819--11848.
  • Károly Böröczky, Mátyás Domokos, Gil Solanes, Dimension of the space of unitary invariant translation invariant tensor valuations, J. Funct. Anal. 280 (2021), no. 4.
  • Gil Solanes, Thomas Wannerer, Integral geometry of exceptional spheres, J. Differential Geom. 117 (2021), no. 1, 137--191.
  • Andreas Bernig, Joseph H.G. Fu, Gil Solanes, Dual curvature measures in hermitian integral geometry, in Analytic Aspects of Convexity, Springer INdAM Series vol.25, Springer (2018).
  • Jun O'Hara, Gil Solanes, Regularized Riesz energies of submanifolds, Math. Nachr. 291 (2018), no. 8-9, 1356--1373.
  • Andreas Bernig, Gil Solanes, Kinematic formulas on the quaternionic plane, Proc. Lond. Math. Soc. 115 (2017), no. 4, 725--762.
  • Gil Solanes, Contact measures in isotropic spaces, Adv. Math. 317 (2017), 645--664.
  • Jun O'Hara, Gil Solanes, Möbius invariant energies and average linking with circles, Tohoku Math. Journal 67 (2015) no. 1, 51--82.
  • Andreas Bernig, Gil Solanes, Classification of invariant valuations on the quaternionic plane, J. Funct. Anal. 267 (2014), no. 8, 2933--2961.
  • Andreas Bernig, Joseph H.G. Fu, Gil Solanes, Integral geometry of complex space forms, Geom. Funct. Anal. 24 (2014), no. 2, 403--492.
  • Gil Solanes, Eberhard Teufel, Horo-tightness and total (absolute) curvatures in hyperbolic spaces, Israel J. Math. 194 (2013), no. 1, 427--459.
  • Eduardo Gallego, Gil Solanes, Eberhard Teufel, Linear combinations of hypersurfaces in hyperbolic space, Monatsh. Math. 169 (2013), no. 3-4, 329--354.
  • Judit Abardia, Eduardo Gallego, Gil Solanes, The Gauss-Bonnet theorem and Crofton-type formulas in complex space forms, Israel J. Math. 187 (2012), 287--315.
  • Gil Solanes, Average linking with complex subspaces, Differential Geom. Appl. 29 (2011), no. 5, 653--659.
  • Wolfgang Kühnel, Gil Solanes, Tight surfaces with boundary, Bull. Lond. Math. Soc. 43 (2011), no. 1, 151--163.
  • Rémi Langevin, Gil Solanes, The geometry of canal surfaces and the length of curves in de Sitter space, Adv. Geom. 11 (2011), no. 4, 585--601.
  • Gil Solanes, Total curvature of complete surfaces in hyperbolic space, Adv. Math. 225 (2010), no. 2, 805--825.
  • E. Gallego, A. Reventós, G. Solanes, E. Teufel, A kinematic formula for the total absolute curvature of intersections, Adv. Geom. 10 (2010), no. 4, 709--718.
  • E. Gallego, A. Reventós, G. Solanes, E. Teufel, Width of convex bodies in spaces of constant curvature, Manuscripta Math. 126 (2008), no. 1, 115--134.
  • Carlos A. Escudero, Agustí Reventós, Gil Solanes, Focal sets in two-dimensional space forms, Pacific J. Math. 233 (2007), no. 2, 309--320.
  • Gil Solanes, Total absolute curvature and tight submanifolds in hyperbolic space, J. Lond. Math. Soc. (2) 75 (2007), no. 2, 420--430.
  • Luis J. Alías, Takashi Kurose, Gil Solanes, Hadamard-type theorems for hypersurfaces in hyperbolic spaces, Differential Geom. Appl. 24 (2006), no. 5, 492--502.
  • Gil Solanes, Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces, Trans. Amer. Math. Soc. 358 (2006), no. 3, 1105--1115 (electronic).
  • Gil Solanes, Eberhard Teufel, Integral geometry in constant curvature Lorentz spaces, Manuscripta Math. 118 (2005), no. 4, 411--423.
  • Eduardo Gallego, Gil Solanes, Integral geometry and geometric inequalities in hyperbolic space, Differential Geom. Appl. 22 (2005), no. 3, 315--325.
  • Gil Solanes, Integral geometry of equidistants in hyperbolic space, Israel J. Math. 145 (2005), 271--284.
  • Eduardo Gallego, Antonio M. Naveira, Gil Solanes, Horospheres and convex bodies in n-dimensional hyperbolic space, Geom. Dedicata 103 (2004), 103--114.
  • Rémi Langevin, Gil Solanes, On bounds for total absolute curvature of surfaces in hyperbolic 3-space, C. R. Math. Acad. Sci. Paris 336 (2003), no. 1, 47--50.
  • Eduardo Gallego, Gil Solanes, Perimeter, diameter and area of convex sets in the hyperbolic plane, J. London Math. Soc. (2) 64 (2001), no. 1, 161--178.

    • Notes

  • Integral geometry of complex space forms, Frankfurt, July 2012.