Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions

被引：5

作者：

Anada, K ^{[1
]}

机构：

[1] Waseda Univ, Dept Appl Phys, Tokyo 1698555, Japan

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2001年 / 12卷 / 02期

关键词：

D O I：

10.1007/PL00009908

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the evolution equations F-t = -(H-l)(alpha)nu, where 0 < <alpha> < 1, <nu> is the unit outer normal vector and H-1 is the harmonic mean curvature defined by H-1 = ((K-1(-1) + K-2(-1))/2)(-1) In this paper, we prove the nonuniqueness of their strictly convex self similar solutions for some 0 < <alpha> < 1. This result implies that there are non-spherical self similar solutions.

引用

页码：109 / 116

页数：8

共 8 条

[1] HARNACK INEQUALITIES FOR EVOLVING HYPERSURFACES [J].