Spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean spaces

被引：9

作者：

Adames, Marcio Rostirolla ^{[1
]}

机构：

[1] UTFPR, Dept Acad Matemat, BR-80230901 Curitiba, PR, Brazil

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2014年 / 22卷 / 05期

关键词：

MINKOWSKI SPACE; SINGULARITIES; CONSTRUCTION; CODIMENSION; SURFACES;

D O I：

10.4310/CAG.2014.v22.n5.a6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cases. The classification is analogous to the existing classification in the Euclidean case [20, 27].

引用

页码：897 / 929

页数：33

共 29 条

[1] ABRESCH U, 1986, J DIFFER GEOM, V23, P175
[2] Adames M.R., 2012, SPACELIKE SELF SIMIL
[3] Anciaux H, 2006, GEOMETRIAE DEDICATA, V120, P37, DOI 10.1007/s10711-006-9082-z
[4] Angenent Sigurd B., 1992, PROGR NONLINEAR DIFF, V7, P21
[5] [Anonymous], 1983, SEMIRIEMANNIAN GEOME
[6] [Anonymous], 2006, Grad. Stud. Math
[7] Baker C., 2011, PREPRINT
[8] BERGNER M, 2011, DISCRETE CONT S SEP, P155
[9] BRAKKE KA, 1978, MATH NOTES, V20
[10] A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
Cao, Huai-Dong
Li, Haizhong
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2013, 46 (3-4) : 879 - 889

← 1 2 3 →