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.

PDF arc_der_mat_113-2_213_2019.pdf - Published Version Restricted to Registered users only Download (350kB) | Request a copy

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
Publication:	ARCHIV DER MATHEMATIK
Publisher:	SPRINGER BASEL AG
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
Date Deposited:	09 Sep 2019 10:40
Last Modified:	09 Sep 2019 10:40
URI:	http://eprints.iisc.ac.in/id/eprint/63297

Actions (login required)

View Item