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

Koichi Anada

doi:10.1007/PL00009908

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

Koichi Anada

Waseda University Senior High School

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider the evolution equations F_t = -(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 language	English
Pages (from-to)	109-116
Number of pages	8
Journal	Calculus of Variations and Partial Differential Equations
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/PL00009908
Publication status	Published - 2001 Mar

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/PL00009908

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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.",

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AB - 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.

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