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

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

Fingerprint

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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, 12(2), 109-116. https://doi.org/10.1007/PL00009908

@article{6a7207c2d19a47c29ceaa1d61bd93986,

title = "Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions",

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.",

author = "Koichi Anada",

year = "2001",

month = mar,

doi = "10.1007/PL00009908",

language = "English",

volume = "12",

pages = "109--116",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Contraction of surfaces by harmonic mean curvature flows and nonuniqueness of their self similar solutions

AU - Anada, Koichi

PY - 2001/3

Y1 - 2001/3

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0005868621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0005868621&partnerID=8YFLogxK

U2 - 10.1007/PL00009908

DO - 10.1007/PL00009908

M3 - Article

AN - SCOPUS:0005868621

VL - 12

SP - 109

EP - 116

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 2

ER -

Access to Document

10.1007/PL00009908