A new variational characterization of the Wulff shape

DOI10.1016/j.difgeo.2007.11.030zbMath1146.53035OpenAlexW2141212365WikidataQ115357624 ScholiaQ115357624MaRDI QIDQ931145

Haizhong Li, Yijun He

Publication date: 25 June 2008

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2007.11.030

zbMATH Keywords

Wulff shape\(F\)-Weingarten operator\(r\)th anisotropic mean curvatureanisotropic principal curvature

Mathematics Subject Classification ID

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

Related Items (13)

Rigidity of complete hypersurfaces in the Euclidean space via anisotropic mean curvatures ⋮ Stability of hypersurfaces with constant \((r+1)\)-th anisotropic mean curvature ⋮ Stable hypersurfaces as minima of the integral of an anisotropic mean curvature preserving a linear combination of area and volume ⋮ Upper bounds for the first eigenvalue of the Laplacian of hypersurfaces in terms of anisotropic mean curvatures ⋮ Some new characterizations of the Wulff shape ⋮ Complete surfaces of constant anisotropic mean curvature ⋮ On almost stable linear Weingarten hypersurfaces ⋮ Stability of area-preserving variations in space forms ⋮ Upper bounds for the first eigenvalue of a Jacobi type operator via anisotropic mean curvatures ⋮ Stable hypersurfaces via the first eigenvalue of the anisotropic Laplacian operator ⋮ Anisotropic eigenvalues upper bounds for hypersurfaces in weighted Euclidean spaces ⋮ Anisotropic version of a theorem of H. Hopf ⋮ Surfaces of constant anisotropic mean curvature with free boundary in revolution surfaces

Cites Work

• Global rigidity theorems of hypersurfaces
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• The Wulff shape minimizes an anisotropic Willmore functional
• \(r\)-minimal submanifolds in space forms
• A note on the stability of the Wulff shape
• Minkowskische Integralformeln und ihre Anwendungen in der Differentialgeometrie im Großen
• Geometry and stability of surfaces with constant anisotropic mean curvature
• Crystalline variational problems
• Stability of the Wulff shape
• Some integral formulas for closed hypersurfaces
• Hypersurfaces with constant scalar curvature in space forms
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