On stable complete hypersurfaces with vanishing r-mean curvature

被引：5
|
作者：
Do Carmo, M
Elbert, MF
机构：
[1] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil
[2] Fed Univ Rio De Janeiro, Inst Matemat, BR-21941590 Rio De Janeiro, Brazil
来源：
TOHOKU MATHEMATICAL JOURNAL | 2004年 / 56卷 / 02期
关键词：
D O I：
10.2748/tmj/1113246548
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A form of Bernstein theorem states that a complete stable minimal surface in euclidean space is a plane. A generalization of this statement is that there exists no complete stable hypersurface of an n-euclidean space with vanishing (n - I)-mean curvature and nowhere zero Gauss-Kronecker curvature. We show that this is the case, provided the immersion is proper and the total curvature is finite.
引用
收藏
页码：155 / 162
页数：8
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