Comptes Rendus
Differential Geometry
Some characterizations of the Wulff shape
[Sur certaines caractérisations des formes de Wulff]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 997-1000.

Étant donné une fonction positive F sur Sn qui vérifie une condition de convexité convenable, nous considérons la r-ième courbure moyenne anisotrope pour les hypersurfaces de Rn+1 qui est une généralisation de la r-ième courbure moyenne usuelle Hr. 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 Sn which satisfies a suitable convexity condition, we consider the r-th anisotropic mean curvature for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. 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.

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Accepté le :
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DOI : 10.1016/j.crma.2010.07.028

Leyla Onat 1

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