Sphères à courbure moyenne constante et problème isopérimétrique dans les variétés homogènes
Séminaire de théorie spectrale et géométrie, Tome 28 (2009-2010), pp. 13-27.

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.

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.

DOI : 10.5802/tsg.276
Classification : 53A10, 53C42, 53A35
Mot clés : Courbure moyenne, variété riemannienne homogène, problème isopérimétrique, théorème de Hopf, théorème d’Alexandrov
Mots clés : Mean curvature, homogeneous Riemannian manifold, isoperimetric problem, Hopf theorem, Alexandrov theorem
Daniel, Benoît 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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Daniel, Benoît. Sphères à courbure moyenne constante et problème isopérimétrique dans les variétés homogènes. Séminaire de théorie spectrale et géométrie, Tome 28 (2009-2010), pp. 13-27. doi : 10.5802/tsg.276. http://archive.numdam.org/articles/10.5802/tsg.276/

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