On the compactness of constant mean curvature hypersurfaces with finite total curvature

被引：16

作者：

do Carmo, MP ^{[1
]}

Cheung, LF

Santos, W

机构：

[1] IMPA, Estrada Dona Castorina 110,Jardim Bot, BR-22460320 Rio De Janeiro, Brazil

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Peoples R China

[3] Univ Fed Rio de Janeiro, Dept Matemat, BR-21945970 Rio De Janeiro, Brazil

来源：

ARCHIV DER MATHEMATIK | 1999年 / 73卷 / 03期

关键词：

Space Form; Curvature Vector; Total Curvature; Curvature Hypersurface; Finite Total Curvature;

D O I：

10.1007/PL00000402

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work we consider a complete submanifold M with parallel mean curvature vector h immersed in a space form of constant sectional curvature c less than or equal to 0. If M has finite total curvature and \H\(2) > -c, we prove that M must be compact.

引用

页码：216 / 222

页数：7

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