Stability index jump for constant mean curvature hypersurfaces of spheres

被引：4

作者：

Perdomo, Oscar ^{[1
]}

Brasil, Aldir, Jr. ^{[2
]}

机构：

[1] Cent Connecticut State Univ, Dept Math, New Britain, CT 06050 USA

[2] Univ Fed Ceara, Dept Matemat, Fortaleza, Ceara, Brazil

来源：

ARCHIV DER MATHEMATIK | 2012年 / 99卷 / 05期

关键词：

Constant mean curvature; Stability index; Spheres; RIEMANNIAN-MANIFOLDS;

D O I：

10.1007/s00013-012-0437-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that the totally umbilical hypersurfaces in the (n + 1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. That is, a compact hypersurface with constant mean curvature, cmc, in S (n+1), different from an Euclidean sphere, must have stability index greater than or equal to 1. In this paper we prove that the weak stability index of any non-totally umbilical compact hypersurface with cmc cannot take the values 1, 2, 3 . . . , n.

引用

页码：493 / 500

页数：8

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