A gap theorem for minimal submanifolds in Euclidean space

被引：1

作者：

Zhao, Entao ^{[1
,2
]}

Cao, Shunjuan ^{[3
]}

机构：

[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

[2] Taipei Off, Natl Ctr Theoret Sci, Taipei 10617, Taiwan

[3] Zhejiang Agr & Forestry Univ, Dept Math, Linan 311300, Peoples R China

来源：

COMPTES RENDUS MATHEMATIQUE | 2015年 / 353卷 / 02期

基金：

中国国家自然科学基金;

关键词：

MEAN-CURVATURE; PROOF;

D O I：

10.1016/j.crma.2014.11.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for a complete minimal submanifold M-n immersed in the Euclidean space Rn+d, if the second fundamental form A and the intrinsic distance function r from a fixed point satisfy r(x)vertical bar A vertical bar(x) <= epsilon for all x is an element of M, where epsilon is a positive constant depending only on n, then M is an affine subspace of Rn+d. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：173 / 177

页数：5

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