Gérard Besson

This article deals with the mathematician, for the historian see Gérard Besson (historian)

Gérard Besson (born December 13, 1955 ) is a French mathematician who deals with differential geometry. He is a professor at the University of Grenoble .

Besson received his doctorate in 1979 under Marcel Berger at the University of Paris VII (Thèse de troisième cycle: Sur la multiplicité de la première valeur propre des surfaces riemanniennes) and habilitated in Grenoble in 1987 (Doctorat d'Etat: Contributions à l'étude des propriétés spectrales des variétés riemanniennes).

Among other things, he dealt with the geometry program of William Thurston (and the methods of Richard S. Hamilton and Grigori Perelman on Ricci flows to prove it), with the spectrum of the Laplace operator on Riemannian manifolds (topic of his dissertation), questions of rigidity, Inequalities for entropy and isoperimetric inequalities .

In 1985, together with Sylvestre Gallot and Pierre Bérard , he found a form of the isoperimetric inequality in Riemannian manifolds depending on a lower bound for the Ricci curvature and the diameter. In 1995 he and Gallot and Gilles Courtois proved an inequality for the volume entropy of locally symmetrical spaces of negative curvature, which in turn provided a new, simpler proof of the rigidity theorem of George Mostow (1968), which states that compact hyperbolic manifolds in more than two dimensions by their Fundamental group are determined except for isometry.

He gave the Bourbaki seminars on the proof of the Poincaré conjecture by Perelman and Hamilton and the theorem of spheres according to Brendle , Schoen .

Fonts

• with Laurent Bessières, Michel Boileau, Sylvain Maillot, Joan Porti Geometrization of 3-manifolds , EMS Tracts in Mathematics, European Mathematical Society 2010
• with L. Bessières, Michel Boileau , S. Maillot, J. Porti, Collapsing irreducible 3-manifolds with nontrivial fundamental group , Inventiones Mathematicae, 179, 2010, pp. 435–446
• with Pierre Bérard, Sylvestre Gallot Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov , Inventiones Mathematicae, Volume 80, 1985, pp. 295–308,
• with P. Bérard, S. Gallot Embedding riemannian manifolds by their heat kernel , Geometric and Functional Analysis (GAFA), 4, 1994, pp. 373-398
• Sur la multiplicity de la première value propre des surfaces riemanniennes, Ann. Inst. Fourier, 30, 1980, pp. 109-128, numdam (dissertation)
• with Gilles Courtois, S. Gallot Le volume et l'entropie minimal des espaces localement symétriques , Inventiones Mathematicae, 103, 1991, pp. 417-445
• with G. Courtois, S. Gallot: Les variétés hyperboliques sont des minima locaux de l'entropie topologique, Inventiones Mathematicae 177, 1994, pp. 403-445
• with G. Courtois, S. Gallot: Volume et entropie minimales des variétés localement symétriques, GAFA 5, 1995, pp. 731-799
• with G. Courtois, S. Gallot: A simple proof of Mostow's rigidity theorem, Ergodic Theory and Dynamical Systems, 16, 1996, pp. 623-649
• Geometry of connections I: an asymptotic expansion for the heat kernel associated with a connection.

Web links

• Homepage at the Fourier Institute
• Author profile in the database zbMATH

Individual evidence

1. ↑ Biographical data from Bibliothèque Nationale de France
2. ↑ See Marcel Berger A panoramic view of Riemannian Geometry , Springer Verlag 2002, p. 343
3. ↑ Berger, A Panoramic view .., p. 510
4. ↑ Pierre Pansu Volume, courbure et entropie, d'après Besson, Courtois et Gallot, Seminaire Bourbaki 823, 1996/97, numdam ( Memento of the original from June 10, 2015 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
5. ↑ Besson, Bourbaki Seminar 2004/05 ( Memento of the original of April 16, 2014 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.