Immersed hypersurfaces with constant Weingarten curvature

DOI10.1007/BF01446438zbMath0643.53043OpenAlexW2062227254MaRDI QIDQ1101979

Gerhard Huisken, Klaus Ecker

Publication date: 1989

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164511

zbMATH Keywords

principal curvaturesisoparametric hypersurfacenon-negative sectional curvaturegeneralized mean curvature functionharmonic means function

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25)

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Cites Work

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• Compact hypersurfaces with a constant higher mean curvature function
• Counterexample to a conjecture of H. Hopf
• Compact hypersurfaces with constant scalar curvature and a congruence theorem
• Sphere theorems via Alexandrov for constant Weingarten curvature hypersurfaces. Appendix to a note of A. Ros
• Symmetric submanifolds of Euclidean space
• Local rigidity theorems for minimal hypersurfaces
• A formula of Simons' type and hypersurfaces with constant mean curvature
• Familles de surfaces isoparametriques dans les espaces à courbure constante
• Submanifolds with Constant Mean Curvature
• Analytic Inequalities