Publications

Sprectrum of the Laplacian and Isoperimetric inequalities

  • Besson, Gérard Sur la multiplicité de la première valeur propre des surfaces riemanniennes. (French) Ann. Inst. Fourier (Grenoble) 30 (1980), no. 1, x, 109–128. (Reviewer: R. Osserman) 58G25 (30F10 53C20)
  • Bérard, P.; Besson, G. Spectres et groupes cristallographiques. II. Domaines sphériques. (French) Ann. Inst. Fourier (Grenoble) 30 (1980), no. 3, 237–248. (Reviewer: P. Günther) 58G25 (10J25 35P20)
  • Bérard, Pierre; Besson, Gérard Remark on an article: “A universal inequality for the first eigenvalue of the Laplacian” [Bull. Soc. Math. France 107 (1979), no. 1, 3–9; MR 80f:58046] by M. Berger. (French) Bull. Soc. Math. France 108 (1980), no. 3, 333–336. (Reviewer: R. S. Millman) 58G25
  • Bérard, P.; Besson, G.; Gallot, S. Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov. (French) [An isoperimetric inequality generalizing the Paul Lévy-Gromov inequality] Invent. Math. 80 (1985), no. 2, 295–308. (Reviewer: Domenico Perrone) 58C40 (53C20 58G25)
  • Besson, Gérard Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou. (French) [Asymptotic behavior of the eigenvalues of the Laplacian in a domain with a hole] Bull. Soc. Math. France 113 (1985), no. 2, 211–230. (Reviewer: Jürgen Eichhorn) 58G25 (35P20)
  • Besson, G. A Kato type inequality for Riemannian submersions with totally geodesic fibers. Ann. Global Anal. Geom. 4 (1986), no. 3, 273–289. (Reviewer: Jürgen Eichhorn) 58G25 (53C42 58G11)
  • Besson, Gérard Propriétés génériques des fonctions propres et multiplicité. (French) [Generic properties of eigenfunctions, and multiplicity] Comment. Math. Helv. 64 (1989), no. 4, 542–588. (Reviewer: Bruno Colbois) 58G25 (35P99 53C42
  • Bérard, P.; Besson, G. Number of bound states and estimates on some geometric invariants. J. Funct. Anal. 94 (1990), no. 2, 375–396. (Reviewer: Józef Dodziuk) 58G30 (53C21 58G25)
  • Besson, Gérard; Bordoni, Manlio On the spectrum of Riemannian submersions with totally geodesic fibers. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 1 (1990), no. 4, 335–340. (Reviewer: Stig I. Andersson) 58G25 (53C12 58G03)
  • Bérard, P.; Besson, G.; Gallot, S. Embedding Riemannian manifolds by their heat kernel. Geom. Funct. Anal. 4 (1994), no. 4, 373–398. (Reviewer: Alberto G. Setti) 58G11 (53C20 58D17 58G30)
  • Besson, Gérard; Colbois, Bruno; Courtois, Gilles Sur la multiplicité de la première valeur propre de l’opérateur de Schrödinger avec champ magnétique sur la sphère $S^2$. (French) [Multiplicity of the first eigenvalue of the Schrödinger operator with magnetic field on the sphere $S^2$] Trans. Amer. Math. Soc. 350 (1998), no. 1, 331–345. (Reviewer: Robert Brooks) 58G25

Rigidity

  • Besson, G.; Courtois, G.; Gallot, S. Volume et entropie minimale des espaces localement symétriques. (French) [Volume and minimal entropy of locally symmetric spaces] Invent. Math. 103 (1991), no. 2, 417–445. (Reviewer: Robert Brooks) 58D17 (53C23 58E11)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Les variétés hyperboliques sont des minima locaux de l’entropie topologique. (French) [Hyperbolic manifolds are local minima of topological entropy] Invent. Math. 117 (1994), no. 3, 403–445. (Reviewer: Vadim A. Kaĭmanovich) 53C20 (53C21 58D17 58F17 58G32)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Volumes, entropies et rigidités des espaces localement symétriques de courbure strictement négative. (French) [Volumes, entropies and rigidities of negatively curved locally symmetric spaces] C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 1, 81–84. (Reviewer: Noureddine Rahmani) 53C20 (53C21)
  • Besson, G.; Courtois, G.; Gallot, S. Entropies et rigidités des espaces localement symétriques de courbure strictement négative. (French) [Entropy and rigidity of locally symmetric spaces with strictly negative curvature] Geom. Funct. Anal. 5 (1995), no. 5, 731–799. (Reviewer: Boris Hasselblatt) 58F17 (53C21 53C35)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Minimal entropy and Mostow’s rigidity theorems. Ergodic Theory Dynam. Systems 16 (1996), no. 4, 623–649. (Reviewer: Boris Hasselblatt) 58F17 (53C20 53C35 58F11 58F18)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Lemme de Schwarz réel et applications géométriques. (French) [The real Schwarz lemma and geometric applications] Acta Math. 183 (1999), no. 2, 145–169. (Reviewer: Andrea Sambusetti) 53C20 (32Q45 53C24)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Hyperbolic manifolds, amalgamated products and critical exponents. C. R. Math. Acad. Sci. Paris 336 (2003), no. 3, 257–261. 57M50 (20E06)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Inégalités de Milnor-Wood géométriques. (French) [Geometric Milnor-Wood inequalities] Comment. Math. Helv. 82 (2007), no. 4, 753–803. (Reviewer: Christopher Connell) 53C24 (20C15 53C35)
  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvain Rigidity of amalgamated products in negative curvature. J. Differential Geom. 79 (2008), no. 3, 335–387. (Reviewer: Gilles Carron) 53C24 (37D40 53C21)

Growth of groups

  • Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre Growth of discrete groups of isometries in negative curvature: a gap-property. C. R. Math. Acad. Sci. Paris 341 (2005), no. 9, 567–572. (Reviewer: Vicente Miquel) 53C20 (53C21)

Geometric Flows

  • L. Bessières, G. Besson,  M. Boileau, S. Maillot,  J. Porti,  Collapsing irreducible 3-manifolds with nontrivial fundamental group, Invent math (2010) 179: 435–460.

Publications in conference proceedings and seminars

  • Besson G., A Generalization of a Faber-Krahn’s inequality, in Spectra of Riemannian Manifolds, Kaigai Publications|Tokyo (1983), 29–37.
  • Besson, Gérard Fibrés vectoriels et principaux: notions de base. (French) [Principal and vector bundles: basic notions] Séminaire de Théorie Spectrale et Géométrie, Année 1983–1984, II.1–II.18, Univ. Grenoble I, Saint-Martin-d’Hères, 1984. (Reviewer: Walter Seaman) 53C05 (53C10 58G25)
  • Bérard, Pierre; Besson, Gérard Théorèmes de finitude en géométrie riemannienne et structures métriques. (French) [Finiteness theorems in Riemannian geometry and metric structures] Séminaire de Théorie Spectrale et Géométrie, Année 1983–1984, VIII.1–VIII.15, Univ. Grenoble I, Saint-Martin-d’Hères, 1984. (Reviewer: Maria Helena Noronha) 53C20
  • Anné, Colette; Besson, Gérard Sur le théorème de l’indice d’après Ezra Getzler. (French) [On the index theorem, following Ezra Getzler] Séminaire de Théorie Spectrale et Géométrie, Année 1984–1985, II.1–II.32, Univ. Grenoble I, Saint-Martin-d’Hères, 1985. 58G10 (57R99 58G15)
  • Besson G., Symmetrization, Appendix  to  Spectral geometry : direct and inverse problems by P. Bérard, Lecture notes in Mathematics, 1207 (1986).
  • Besson, Gérard On symmetrization. Nonlinear problems in geometry (Mobile, Ala., 1985), 9–21, Contemp. Math., 51, Amer. Math. Soc., Providence, RI, 1986. (Reviewer: Yoshiaki Maeda) 58G11 (53C20 58C40 58G25)
  • Besson, Gérard Sur la multiplicité des valeurs propres du laplacien. (French) [On the multiplicity of eigenvalues of the Laplacian] Séminaire de Théorie Spectrale et Géométrie, No. 5, Année 1986–1987, 107–132, Univ. Grenoble I, Saint-Martin-d’Hères, 1987. (Reviewer: Bruno Colbois) 58G25 (35P99)
  • Besson, Gérard On the multiplicity of the eigenvalues of the Laplacian. Geometry and analysis on manifolds (Katata/Kyoto, 1987), 32–53, Lecture Notes in Math., 1339, Springer, Berlin, 1988. (Reviewer: Carolyn Gordon) 58G25
  • Bérard, P. H.; Besson, G. On the number of bound states and estimates on some geometric invariants. Partial differential equations (Rio de Janeiro, 1986), 30–40, Lecture Notes in Math., 1324, Springer, Berlin, 1988. 58G25 (53C21 58G30)
  • Besson G., Sur la cohomologie bornée, séminaire de cohomologie bornée, E.N.S. Lyon (1988).
  • Besson, Gérard L’entropie minimale des espaces symétriques. (French) [Minimal entropy of symmetric spaces] Séminaire de Théorie Spectrale et Géométrie, No. 8, Année 1989–1990, 77–88, Sémin. Théor. Spectr. Géom., 8, Univ. Grenoble I, Saint-Martin-d’Hères, 1990. 37D40 (37B40 37C40)
  • Besson, Gérard Ergodicité du flot géodésique des surfaces riemanniennes à courbure $-1$. (French) [Ergodicity of the geodesic flow of Riemannian surfaces with curvature equal to $-1$] Rencontres de Théorie Spectrale et Géométrie (Aussois, 1991), 25–31, Univ. Grenoble I, Saint-Martin-d’Hères, 1991. 37D40 (37C40)
  • Besson, Gérard; Lohkamp, Joachim; Pansu, Pierre; Petersen, Peter Riemannian geometry. Papers from the micro-program held in Waterloo, Ontario, August 3–13, 1993. Edited by Miroslav Lovrić, Maung Min-Oo and McKenzie Y.-K. Wang. Fields Institute Monographs, 4. American Mathematical Society, Providence, RI, 1996. xii+115 pp. ISBN: 0-8218-0263-1 53-06
  • Besson, Gérard Volumes and entropies. Riemannian geometry (Waterloo, ON, 1993), 1–22, Fields Inst. Monogr., 4, Amer. Math. Soc., Providence, RI, 1996. (Reviewer: Boris Hasselblatt) 53C20 (58F17)
  • Besson G., Volumes and Rigidities of Riemannian Manifolds, Lecture Notes of the Thirteen Kaist Math. Workshop, (1998), 135-164.
  • Besson, Gérard From isoperimetric inequalities to heat kernels via symmetrisation. Surveys in differential geometry. Vol. IX, 27–51, Surv. Differ. Geom., IX, Int. Press, Somerville, MA, 2004. 58J35 (58J53
  • Besson, G. The geometrization conjecture after R. Hamilton and G. Perelman. Rend. Semin. Mat. Univ. Politec. Torino 65 (2007), no. 4, 397–411. (Reviewer: John Urbas) 53C44 (57M40 57M50)
  • Besson, G. On the geometrisation conjecture. Boll. Unione Mat. Ital. (9) 2 (2009), no. 1, 245–257. 57Mxx (53Cxx 57Nxx)

Vulgarisation

Bourbaki seminars

  • Besson, Gérard Preuve de la conjecture de Poincaré en déformant la métrique par la courbure de Ricci (d’après G. Perelʹman). (French) [Proving the Poincaré conjecture by deforming the metric by the Ricci curvature (after G. Perelʹman)] Séminaire Bourbaki. Vol. 2004/2005. Astérisque No. 307 (2006), Exp. No. 947, ix, 309–347. (Reviewer: Esther Cabezas Rivas) 53C44 (53C21 57M40)
  • Besson, Gérard Le théorème de la sphère différentiable (d’après S. Brendle et R. Schoen). (French) [The Differentiable Sphere Theorem  (after S. Brendle and R. Schoen)] Séminaire Bourbaki. 61ème année,  Vol. 2008/2009, n° 1003 (March 2009).

Book

  • L. Bessières,  G. Besson,  M. Boileau, S. Maillot,  J. Porti, The Geometrisation of 3-manifolds, to be published in 2010.

Submitted

In preparation

  • Besson G., Courtois G. et Gallot S., Un lemme de Margulis sans courbure.
  • Besson G., Geometry of connections I : an asymptotic expansion for the heat kernel associated to a connection.
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