Backwards uniqueness of the mean curvature flow

被引：2
|
作者：
Huang, Hong [1 ]
机构：
[1] Beijing Normal Univ, Lab Math & Complex Syst, Minist Educ, Sch Math Sci, Beijing 100875, Peoples R China
来源：
GEOMETRIAE DEDICATA | 2019年 / 203卷 / 01期
关键词：
Mean curvature flow; Backwards uniqueness; Second fundamental form;
D O I：
10.1007/s10711-019-00424-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we prove the backwards uniqueness of the mean curvature flow for (codimension one) hypersurfaces in a Euclidean space. More precisely, let F-t, (F) over tilde (t):M-n -> Rn+1 be two complete solutions of the mean curvature flow on M-n x [0, T] with bounded second fundamental forms. Suppose F-T = (F) over tilde (T), then F-t = (F) over tilde (t) on M-n x [0, T]. This is an analog of a result of Kotschwar on the Ricci flow.
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页码：67 / 71
页数：5
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