Willmore surfaces in Sn

被引：32

作者：

Li, HZ ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2002年 / 21卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Willmore surface; minimal surface; pinching; Veronese surface;

D O I：

10.1023/A:1014759309675

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A surface x: M --> S-n is called a Willmore surface if it is a critic al surface of the Willmore functional. It is well known that any minimal surface is a Willmore surface and that many nonminimal Willmore surfaces exists. In this paper, we establish an integral inequality for compact Willmore surfaces in S-n and obtain a new characterization of the Veronese surface in S-4 as a Willmore surface. Our result reduces to a well-known result in the case of minimal surfaces.

引用

页码：203 / 213

页数：11

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