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Stability of generalized linear Weingarten hypersurfaces immersed in the Euclidean space
da Silva, Jonatan F. (Universidade Federal do Ceará (Brasil). Departamento de Matemática)
de Lima, Henrique F. (Universidade Federal de Campina Grande. Departamento de Matemática)
Velásquez, Marco Antonio L. (Universidade Federal de Campina Grande. Departamento de Matemática)

Date: 2018
Abstract: Given a positive function F defined on the unit Euclidean sphere and satisfying a suitable convexity condition, we consider, for hypersurfaces Mn immersed in the Euclidean space Rn+1, the so-called k-th anisotropic mean curvatures HF k, 0 ≤ k ≤ n. For fixed 0 ≤ r ≤ s ≤ n, a hypersurface Mn of Rn+1 is said to be (r, s, F)-linear Weingarten when its k-th anisotropic mean curvatures HF k, r ≤ k ≤ s, are linearly related. In this setting, we establish the concept of stability concerning closed (r, s, F)-linear Weingarten hypersurfaces immersed in Rn+1 and, afterwards, we prove that such a hypersurface is stable if, and only if, up to translations and homotheties, it is the Wulff shape of F. For r = s and F ≡ 1, our results amount to the standard stability studied, for instance, by Alencar–do Carmo–Rosenberg.
Rights: Tots els drets reservats
Language: Anglès.
Document: article ; recerca ; publishedVersion
Subject: Euclidean space ; Wulff shape ; K-th anisotropic mean curvatures ; (r, s, f)-linear weingarten hypersurfaces ; Stable closed hypersurfaces
Published in: Publicacions matemàtiques, Vol. 62 Núm. 1 (2018) , p. 95-111 (Articles) , ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/329929
DOI: 10.5565/PUBLMAT6211805

17 p, 359.4 KB

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Articles > Published articles > Publicacions matemàtiques
Articles > Research articles

 Record created 2017-12-05, last modified 2019-02-02

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