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

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 : https://doi.org/10.5802/tsg.276
Classification:  53A10,  53C42,  53A35
Keywords: Mean curvature, homogeneous Riemannian manifold, isoperimetric problem, Hopf theorem, Alexandrov theorem
@article{TSG_2009-2010__28__13_0,
     author = {Daniel, Beno\^\i t},
     title = {Sph\`eres \`a courbure moyenne constante et probl\`eme isop\'erim\'etrique dans les vari\'et\'es homog\`enes},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {28},
     year = {2009-2010},
     pages = {13-27},
     doi = {10.5802/tsg.276},
     language = {fr},
     url = {http://www.numdam.org/item/TSG_2009-2010__28__13_0}
}
Daniel, Benoît. 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. http://www.numdam.org/item/TSG_2009-2010__28__13_0/

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