A BERNSTEIN TYPE THEOREM FOR ANCIENT SOLUTIONS TO THE MEAN CURVATURE FLOW IN ARBITRARY CODIMENSION

被引：1

作者：

Guan, Li ^{[1
]}

Xu, Hongwei ^{[1
]}

Zhao, Entao ^{[1
]}

机构：

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

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 01期

基金：

中国国家自然科学基金;

关键词：

COMPLETE TRANSLATING SOLITONS;

D O I：

10.1090/proc/16078

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Bernstein type theorem for ancient solutions to the mean curvature flow in higher codimension. More precisely, we show that for a complete ancient solution {M-t}(t is an element of(-infinity,0)), if the mean curvature vector is uniformly bounded and the omega-function for M-t satisfies omega >= omega(0) uniformly for some constant omega(0) > 1/root 2, then M-t must be an affine subspace for each t is an element of(-infinity,0).

引用

页码：269 / 279

页数：11

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