Anisotropic isoparametric hypersurfaces in Euclidean spaces

被引：0
作者：
Jianquan Ge
Hui Ma
机构：
[1] Beijing Normal University,School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems
[2] Tsinghua University,Department of Mathematical Sciences
来源：
Annals of Global Analysis and Geometry | 2012年 / 41卷
关键词：
Wulff shape; Anisotropic mean curvature; Cartan identity; Primary 53C40; Secondary 53A10; 52A20;
D O I：
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摘要：
In this paper, by Nomizu’s method and some technical treatment of the asymmetry of the F-Weingarten operator, we obtain a classification of complete anisotropic isoparametric hypersurfaces, i.e., hypersurfaces with constant anisotropic principal curvatures, in Euclidean spaces, which is a generalization of the classical case for isoparametric hypersurfaces in Euclidean spaces. On the other hand, by an example of local anisotropic isoparametric surface constructed by B. Palmer, we find that in general anisotropic isoparametric hypersurfaces have both local and global aspects as in the theory of proper Dupin hypersurfaces, which differs from classical isoparametric hypersurfaces.
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页码：347 / 355
页数：8
相关论文
共 33 条
[1]  
Brothers J.E.(1994)The isoperimetric theorem for general integrands Michigan Math. J. 41 419-431
[2]  
Morgan F.(2008)Isoparametric and Dupin hypersurfaces SIGMA 4 28-36
[3]  
Cecil T.E.(2004)On surfaces of prescribed F-mean curvature Pacific J. Math. 213 15-118
[4]  
Clarenz U.(1992)Wulff theorem and best constant in Sobolev inequality J. Math. Pures Appl. 71 97-136
[5]  
von der Mosel H.(1991)A uniqueness proof for the Wulff theorem Proc. R. Soc. Edinburgh A. 119 125-619
[6]  
Dacorogna B.(2009)Uniqueness of constant weakly anisotropic mean curvature immersion of Adv. Differential. Equ. 14 601-1314
[7]  
Pfister C.E.(2008) in Illinois J. Math. 52 1301-247
[8]  
Fonseca I.(2009)Stability of hypersurfaces with constant ( Ann. Global Anal. Geom. 35 243-868
[9]  
Müller S.(2009) + 1)-th anisotropic mean curvature Indiana Univ. Math. J. 58 853-1852
[10]  
Giga Y.(2005)Anisotropic version of a theorem of H, Hopf Indiana Univ. Math. J. 54 1817-298
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