Stable constant mean curvature hypersurfaces

DOI10.1090/S0002-9939-07-08825-9zbMath1125.53045MaRDI QIDQ5295120

Maria Fernanda Elbert, Barbara Nelli, Harold Rosenberg

Publication date: 27 July 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

sectional curvaturestability operatordiameter estimatestrongly stable H-hypersurfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (11)

Gap theorems for minimal submanifolds of a hyperbolic space ⋮ Rigidity of complete minimal hypersurfaces in a hyperbolic space ⋮ Stable hypersurfaces with constant scalar curvature ⋮ Existence of regular neighborhoods for \(H\)-surfaces ⋮ Potential theory for manifolds with boundary and applications to controlled mean curvature graphs ⋮ Two rigidity results for stable minimal hypersurfaces ⋮ Limit lamination theorems for \(H\)-surfaces ⋮ Rigidity and stability estimates for minimal submanifolds in the hyperbolic space ⋮ Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds ⋮ A note on constant mean curvature foliations of noncompact Riemannian manifolds ⋮ On the entropies of hypersurfaces with bounded mean curvature

Cites Work

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• Stability of hypersurfaces with constant mean curvature
• On complete minimal surfaces with finite Morse index in three manifolds
• Rigidity of stable minimal hypersurfaces
• Eigenvalue and ``twisted eigenvalue problems, applications to CMC surfaces
• On constant mean curvature hypersurfaces with finite index
• On complete hypersurfaces with constant mean curvature and finite \(L^p\)-norm curvature in \(\mathbb R^{n+1}\)
• Maximum principles at infinity for surfaces of bounded mean curvature in R^3 and H^3

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