Some characterizations of the Wulff shape

Leyla Onat

doi:10.1016/j.crma.2010.07.028

Differential Geometry

Some characterizations of the Wulff shape
[Sur certaines caractérisations des formes de Wulff]

Présenté par : Jean-Pierre Demailly

Leyla Onat ¹

¹ Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 Aydın, Turkey

Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 997-1000.

Résumé
Abstract

Étant donné une fonction positive F sur $S^{n}$ qui vérifie une condition de convexité convenable, nous considérons la r-ième courbure moyenne anisotrope pour les hypersurfaces de $R^{n + 1}$ qui est une généralisation de la r-ième courbure moyenne usuelle $H_{r}$ . En utilisant une formule intégrale de type Minkowski pour les hypersurfaces compactes due à H.J. He et H. Li, nous introduisons de nouvelles caractérisations des formes de Wulff.

For a positive function F on $S^{n}$ which satisfies a suitable convexity condition, we consider the r-th anisotropic mean curvature for hypersurfaces in $R^{n + 1}$ which is a generalization of the usual r-th mean curvature $H_{r}$ . By using an integral formula of Minkowski type for compact hypersurface due to H.J. He and H. Li, we introduce some new characterizations of the Wulff shape.

Reçu le : 2010-04-22
Accepté le : 2010-07-28
Publié le : 2010-08-21

DOI : 10.1016/j.crma.2010.07.028

Affiliations des auteurs :

Leyla Onat ¹

¹ Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 Aydın, Turkey

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     title = {Some characterizations of the {Wulff} shape},
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     language = {en},
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Leyla Onat. Some characterizations of the Wulff shape. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 997-1000. doi : 10.1016/j.crma.2010.07.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.028/

Bibliographie
Cité par

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[4] Y.J. He; H. Li Integral formula of Minkowski type and new characterization of the Wulff shape, Acta Math. Sinica, Volume 24 (2008), pp. 697-704

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