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
收藏
页码：213 / 224
页数：12
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