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On compact anisotropic Weingarten hypersurfaces in Euclidean space

Roth, Julien and Upadhyay, Abhitosh (2019) On compact anisotropic Weingarten hypersurfaces in Euclidean space. In: ARCHIV DER MATHEMATIK, 113 (2). pp. 213-224.

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Official URL: https://dx.doi.org/ 10.1007/s00013-019-01315-8

Abstract

We show that, up to homotheties and translations, the Wulff shape WF is the only compact embedded hypersurface of the Euclidean space satisfying HrF=aHF+b with a0, b>0, where HF and HrF are, respectively, the anisotropic mean curvature and anisotropic r-th mean curvature associated with the function F:Sn?R+. Further, we show that if the L2-norm of HrF-aHF-b is sufficiently close to 0, then the hypersurface is close to the Wulff shape for the W-2,W-2-norm.

Item Type: Journal Article
Additional Information: copyright for this article belongs to SPRINGER BASEL AG
Keywords: Wulff shape; Weingarten hypersurfaces; Anisotropic mean curvature
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 09 Sep 2019 10:40
Last Modified: 09 Sep 2019 10:40
URI: http://eprints.iisc.ac.in/id/eprint/63297

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