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).
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页码：269 / 279
页数：11
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