A note on compact Weingarten hypersurfaces embedded in \(\mathbb{R}^{n + 1}\)

DOI10.1007/s00013-018-1233-6zbMath1402.53004OpenAlexW2888774195MaRDI QIDQ1626644

Eudes Leite de Lima

Publication date: 21 November 2018

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-018-1233-6

zbMATH Keywords

higher-order mean curvatureround sphereWeingarten hypersurface

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Related Items

On compact embedded Weingarten hypersurfaces in warped products ⋮ Some new characterizations of the Wulff shape ⋮ On the higher order mean curvatures of spacelike hypersurfaces in pp-wave spacetimes ⋮ On compact anisotropic Weingarten hypersurfaces in Euclidean space

Cites Work

• A characteristic property of spheres
• New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space
• 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
• Compact hypersurfaces with constant higher order mean curvatures
• Some new characterizations of the Euclidean sphere
• Some integral formulas for closed hypersurfaces

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