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Spheres of constant mean curvature and isoperimetric problems in homogeneous manifolds. (Sphères à courbure moyenne constante et problème isopérimétrique dans les variétés homogènes.) (French. English summary) Zbl 1222.53064
Actes de Séminaire de Théorie Spectrale et Géométrie. Année 2009–2010. St. Martin d’Hères: Université de Grenoble I, Institut Fourier. Séminaire de Théorie Spectrale et Géométrie 28, 13-27 (2010).
Summary: This is a survey on some recent results about existence and uniqueness of constant mean curvature spheres in simply connected homogeneous Riemannian 3-manifolds and their relation to the isoperimetric problem in these manifolds.
For the entire collection see [Zbl 1213.35007].
MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C30 Differential geometry of homogeneous manifolds
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