ENTIRE DOWNWARD TRANSLATING SOLITONS TO THE MEAN CURVATURE FLOW IN MINKOWSKI SPACE

被引：0

作者：

Spruck, Joel ^{[1
]}

Xiao, Ling ^{[2
]}

机构：

[1] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 08期

关键词：

FORCING TERM; HYPERSURFACES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study entire translating solutions u(x) to a mean curvature flow equation in Minkowski space. We show that if {(x,u(x))vertical bar x is an element of R-n} is a strictly spacelike hypersurface, then Sigma reduces to a strictly convex rank k soliton in R-k,R-1 (after splitting off trivial factors) whose "blowdown" converges to a multiple lambda is an element of (0, 1) of a positively homogeneous degree one convex function in R-k. We also show that there is nonuniqueness as the rotationally symmetric solution may be perturbed to a solution by an arbitrary smooth order one perturbation.

引用

页码：3517 / 3526

页数：10