The complete hyper-surfaces with zero scalar curvature in

被引：0

作者：

Li Yaowen ^{[1
]}

Xu Xingwang ^{[2
]}

Zhou Jiuru ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[2] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2013年 / 44卷 / 04期

关键词：

Bernstein type theorems; Scalar curvature; Sobolev inequality; Ends; CONSTANT MEAN-CURVATURE; MINIMAL HYPERSURFACES; EUCLIDEAN-SPACE; SUBMANIFOLDS; RN+1; INEQUALITIES; STABILITY; SOBOLEV;

D O I：

10.1007/s10455-013-9373-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be a complete and noncompact hyper-surface immersed in . We should show that if is of finite total curvature and Ricci flat, then turns out to be a hyperplane. Meanwhile, the hyper-surfaces with the vanishing scalar curvature is also considered in this paper. It can be shown that if the total curvature is sufficiently small, then by refined Kato's inequality, conformal flatness and flatness are equivalent in some sense. And those results should be compared with Hartman and Nirenberg's similar results with flat curvature assumption.

引用

页码：401 / 416

页数：16

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