Sylvestre Gallot
{{Short description|French mathematician (born 1948)}}
Sylvestre F. L. Gallot (born January 29, 1948, in Bazoches-lès-Bray){{cite web|title=Gallot, S.|website=Library of Congress|url=http://id.loc.gov/authorities/names/n86007665.html}}{{cite web|title=Sylvestre Gallot|website=Aracne editrice|url=http://www.aracneeditrice.it/aracneweb/index.php/autori.html?auth-id=243353}} is a French mathematician, specializing in differential geometry. He is an emeritus professor at the Institut Fourier of the Université Grenoble Alpes, in the Geometry and Topology section.{{Cite web|title=Annuaire {{!}} UMR 5582 - Laboratoire de mathématiques|url=https://www-fourier.ujf-grenoble.fr/?q=content/annuaire&projet=Th%C3%A8me+G%C3%A9om%C3%A9trie+et+Topologie|access-date=2020-08-20|website=www-fourier.ujf-grenoble.fr}}
Education and career
Sylvestre Gallot received his doctorate from Paris Diderot University (Paris 7) with thesis under the direction of Marcel Berger.{{MathGenealogy|id=78148|title=Sylvain Gallot}} Gallot worked during the early 1980s at the University of Savoie, then at the École Normale Supérieure de Lyon and the University of Grenoble (Institut Fourier).
His research deals with isoperimetric inequalities in Riemann geometry, rigidity issues, and the Laplace operator spectrum on Riemannian manifolds. With Gérard Besson and Pierre Bérard, he discovered, in 1985, a form of isoperimetric inequality in Riemannian manifolds with a lower bound involving the diameter and Ricci curvature.{{cite book|author=Berger, Marcel|title=A panoramic view of Riemannian geometry|publisher=Springer|year=2007|page=319|isbn=978-3-540-65317-2|url=https://books.google.com/books?id=d_SsagQckaQC&pg=PA319}} (pbk reprint of 2003 original) In 1995, he discovered with Gérard Besson and Gilles Courtois, a Chebyshev inequality for the minimal entropy of locally symmetrical spaces of negative curvature; the inequality gives a new and simpler proof of the Mostow rigidity theorem.{{cite book|title=A panoramic view of Riemann geometry|year=2007|page=484|url=https://books.google.com/books?id=d_SsagQckaQC&pg=PA484|isbn=9783540653172|last1=Berger|first1=Marcel|publisher=Springer }}{{cite journal|author=Pansu, Pierre|authorlink=Pierre Pansu|title=Volume, courbure et entropie, d'après Besson, Courtois et Gallot|journal=Seminaire Bourbaki|volume=1996/97, exposés 820–834, Astérisque, no. 245, Talk no. 823|pages=83–103|url=http://www.numdam.org/item/?id=SB_1996-1997__39__83_0}} The result of Besson, Courtois, and Gallo is called minimal entropy rigidity.{{cite arXiv|author=Connell, Christopher|author2=Farb, Benson|authorlink2=Benson Farb|title=Minimal entropy rigidity for lattices in products of rank one symmetric spaces|year=2001|eprint=math/0101045}}
In 1998 he was an invited speaker with talk Curvature decreasing maps are volume decreasing at the International Congress of Mathematicians in Berlin.{{cite book|author=Gallot, Sylvestre|chapter=Curvature-decreasing maps are volume-decreasing (On joint work with G. Besson and G. Courtois)|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II|year=1998|pages=339–348|chapter-url=https://www.elibm.org/ft/10011711000}}
Selected publications
- with Dominique Hulin, Jacques Lafontaine [https://books.google.com/books/about/Riemannian_Geometry.html?id=6F4Umpws_gUC Riemannian Geometry], Universitext, Springer Verlag, 3rd edition 2004
- with Daniel Meyer Opérateur de courbure et laplacien des formes différentielles d´une variété riemannienne, J. Math. Pures Appliqués, 54, 1975, 259-284
- Inégalités isopérimétriques, courbure de Ricci et invariants géométriques, 1,2, C. R. Acad. Sci., 296, 1983, 333-336, 365-368
- Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Astérisque 163/164, 1988, 33-91
- with Pierre Bérard, Gérard Besson Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov, Inventiones Mathematicae, vol. 80, 1985, pp. 295–308 {{doi|10.1007/BF01388608}}
- with G. Besson, P. Bérard Embedding Riemannian manifolds by their heat kernel, Geometric Functional Analysis (GAFA), 4, 1994, pp. 373–398 {{doi|10.1007/BF01896401}}
- with G. Besson, G. Courtois Volume et entropie minimale des espaces localement symétriques, Inventiones Mathematicae, 103, 1991, pp. 417–445 {{doi|10.1007/BF01239520}}
- with G. Besson, G. Courtois: Les variétés hyperboliques sont des minima locaux de l’entropie topologique, Inventiones Mathematicae 177, 1994, pp. 403–445 {{doi|10.1007/BF01232251}}
- with G. Besson G. Courtois: Volume et entropie minimales des variétés localement symétriques, GAFA 5, 1995, pp. 731–799
- with G. Besson, G. Courtois: [https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/minimal-entropy-and-mostows-rigidity-theorems/7B7F706676FAC80C728846B8A29AFF00 Minimal entropy and Mostow’s rigidity theorems], Ergodic Theory and Dynamical Systems, 16, 1996, pp. 623–649
- Volumes, courbure de Ricci et convergence des variétés, d'après Tobias Colding et Cheeger-Colding, Séminaire Bourbaki 835, 1997/98
References
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Category:20th-century French mathematicians
Category:21st-century French mathematicians
Category:Differential geometers