Some characterizations of the Wulff shape

Leyla Onat

doi:10.1016/j.crma.2010.07.028

Differential Geometry

Some characterizations of the Wulff shape

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2010-04-22
Accepted: 2010-07-28
Published online: 2010-08-21

DOI: 10.1016/j.crma.2010.07.028

Author's affiliations:

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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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/

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