Sphères à courbure moyenne constante et problème isopérimétrique dans les variétés homogènes

Benoît Daniel

doi:10.5802/tsg.276

Benoît Daniel ¹

¹ Université Paris-Est Laboratoire d’Analyse et de Mathématiques Appliquées CNRS UMR 8050 61 avenue du Général de Gaulle 94010 Créteil (France)

Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010), pp. 13-27.

Abstract
Résumé

This is a survey on some recent results about the existence and the uniqueness of constant mean curvature spheres in simply connected homogeneous Riemannian 3-manifolds and their relation to the isoperimetric problem in these manifolds.

Nous passons en revue certains résultats récents sur l’existence et l’unicité des sphères à courbure moyenne constante dans les variétés riemanniennes homogènes simplement connexes de dimension $3$ et leurs liens avec le problème isopérimétrique dans ces variétés.

DOI: 10.5802/tsg.276

Classification: 53A10, 53C42, 53A35
Mot clés : Courbure moyenne, variété riemannienne homogène, problème isopérimétrique, théorème de Hopf, théorème d’Alexandrov
Keywords: Mean curvature, homogeneous Riemannian manifold, isoperimetric problem, Hopf theorem, Alexandrov theorem

Author's affiliations:

Benoît Daniel ¹

¹ Université Paris-Est Laboratoire d’Analyse et de Mathématiques Appliquées CNRS UMR 8050 61 avenue du Général de Gaulle 94010 Créteil (France)

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Benoît Daniel. Sphères à courbure moyenne constante et problème isopérimétrique dans les variétés homogènes. Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010), pp. 13-27. doi : 10.5802/tsg.276. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.276/

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