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

Koichi Anada

Research output: Contribution to journal › Article

3 Citations (Scopus)

Abstract

We consider the evolution equations Ft = -(H-1)αν, where 0 < α < 1, ν is the unit outer normal vector and H-1 is the harmonic mean curvature defined by H-1 = ((κ1 -1 + κ2 -1)/2)-1. In this paper, we prove the nonuniqueness of their strictly convex self similar solutions for some 0 < α < 1. This result implies that there are non-spherical self similar solutions.

Original languageEnglish
Pages (from-to)109-116
Number of pages8
JournalCalculus of Variations and Partial Differential Equations
Volume12
Issue number2
Publication statusPublished - 2001 Mar

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Harmonic mean
Mean Curvature Flow
Self-similar Solutions
Nonuniqueness
Contraction
Normal vector
Strictly Convex
Mean Curvature
Evolution Equation
Imply
Unit

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions. / Anada, Koichi.

In: Calculus of Variations and Partial Differential Equations, Vol. 12, No. 2, 03.2001, p. 109-116.

Research output: Contribution to journal › Article

Anada, K 2001, 'Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions', Calculus of Variations and Partial Differential Equations, vol. 12, no. 2, pp. 109-116.
Anada K. Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions. Calculus of Variations and Partial Differential Equations. 2001 Mar;12(2):109-116.
Anada, Koichi. / Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions. In: Calculus of Variations and Partial Differential Equations. 2001 ; Vol. 12, No. 2. pp. 109-116.
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