Stable hypersurfaces via the first eigenvalue of the anisotropic Laplacian operator

DOI10.1007/s11565-018-0301-yzbMath1400.53010OpenAlexW2798022700WikidataQ130038268 ScholiaQ130038268MaRDI QIDQ1989488

Henrique Fernandes de Lima, Jonatan Floriano da Silva, Marco Antonio L. Velásquez

Publication date: 26 October 2018

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-018-0301-y

zbMATH Keywords

Euclidean spaceJacobi operatorWulff shapeanisotropic mean curvatures\((r, s, F)\)-linear Weingarten surfacesstable closed hypersurfaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25)

Cites Work

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• Stable hypersurfaces as minima of the integral of an anisotropic mean curvature preserving a linear combination of area and volume
• A new variational characterization of the Wulff shape
• Integral formula of Minkowski type and new characterization of the Wulff shape
• Global rigidity theorems of hypersurfaces
• Stability of hypersurfaces with constant \(r\)-mean curvature
• The Wulff shape minimizes an anisotropic Willmore functional
• On the decay of matrix coefficients for exceptional groups
• A note on the stability of the Wulff shape
• Stability of hypersurfaces with constant \((r+1)\)-th anisotropic mean curvature
• Geometry and stability of surfaces with constant anisotropic mean curvature
• Crystalline variational problems
• Stability of the Wulff shape

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