Uniqueness Theorems for Free Boundary Minimal Disks in Space Forms

被引：44

作者：

Fraser, Ailana ^{[1
]}

Schoen, Richard ^{[2
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92617 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 17期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

STABILITY; SURFACES;

D O I：

10.1093/imrn/rnu192

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. Nitsche and R. Souam.

引用

页码：8268 / 8274

页数：7

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