Rigidity theorems for hypersurfaces with constant mean curvature

DOI10.1007/S00574-014-0055-9zbMath1319.53065OpenAlexW1973755162MaRDI QIDQ487037

Josué Meléndez

Publication date: 19 January 2015

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-014-0055-9

zbMATH Keywords

isoparametric hypersurfacesconstant mean curvaturehypersurfacesClifford tori

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (13)

A sharp scalar curvature estimate for CMC hypersurfaces satisfying an Okumura type inequality ⋮ A new optimal estimate for the first stability eigenvalue of closed hypersurfaces in Riemannian space forms ⋮ A sharp integral inequality for compact Weingarten hypersurfaces under an Okumura type inequality ⋮ Integral inequalities for compact hypersurfaces with constant scalar curvature in the Euclidean sphere ⋮ Characterizations of complete CMC spacelike hypersurfaces satisfying an Okumura type inequality ⋮ New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms ⋮ COMPLETE WEINGARTEN HYPERSURFACES SATISFYING AN OKUMURA TYPE INEQUALITY ⋮ Hypersurfaces with constant scalar curvature in space forms ⋮ Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces ⋮ Characterizing closed linear Weingarten spacelike submanifolds immersed in the de Sitter space ⋮ Complete spacelike hypersurfaces with constant scalar curvature: descriptions and gaps ⋮ A gap theorem for constant scalar curvature hypersurfaces ⋮ Revisiting linear Weingarten hypersurfaces immersed into a locally symmetric Riemannian manifold

Cites Work

• A new pinching theorem for closed hypersurfaces with constant mean curvature in \(S^{n+1}\)
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• Hypersurfaces in a sphere with constant mean curvature
• Harmonic functions on complete riemannian manifolds
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• Hypersurfaces with Constant Mean Curvature in Spheres
• Complete rotation hypersurfaces with Hk constant in space forms
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
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