Curve Shortening Flow in Arbitrary Dimensional Euclidian Space

被引：0

作者：

Yun Yan Yang

Xiao Xiang Jiao

机构：

[1] Peking University,School of Mathematical Sciences

[2] Graduate School,Department of Mathematics

[3] Chinese Academy of Sciences,undefined

来源：

Acta Mathematica Sinica | 2005年 / 21卷

关键词：

Curve shortening flow; Singularity formation; Blow up; 53C44;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, curve shortening flow in Euclidian space Rn(n ≥ 3) is studied, and S. Altschuler’s results about flow for space curves are generalized. We prove that the curve shortening flow converges to a straight line in infinite time if the initial curve is a ramp. We also prove the planar phenomenon when the curve shortening flow blows up.

引用

页码：715 / 722

页数：7

共 7 条

[1] Gage undefined(1986)undefined J. Diff. Geom. 23 69-undefined
[2] Altschuler undefined(1992)undefined J. Diff. Geom. 25 283-undefined
[3] Altschuler undefined(1991)undefined J. Diff. Geom. 34 491-undefined
[4] Grayson undefined(1987)undefined J. Diff. Geom. 26 285-undefined
[5] Huisken undefined(1990)undefined J. Diff. Geom. 31 285-undefined
[6] Horn undefined(1971)undefined Amer. Math. Monthly 78 380-undefined
[7] Angenent undefined(1991)undefined Ann. Math. 131 171-undefined

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