On compact anisotropic Weingarten hypersurfaces in Euclidean space

被引：4

作者：

Roth, Julien ^{[1
]}

Upadhyay, Abhitosh ^{[2
]}

机构：

[1] UPEM UPEC, CNRS, Lab Anal & Math Appl, F-77454 Marne La Vallee, France

[2] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

ARCHIV DER MATHEMATIK | 2019年 / 113卷 / 02期

关键词：

Wulff shape; Weingarten hypersurfaces; Anisotropic mean curvature; CURVATURE;

D O I：

10.1007/s00013-019-01315-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：213 / 224

页数：12

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