Differential and Integral Equations

Soliton solutions for the mean curvature flow

N. Hungerbühler and K. Smoczyk

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Abstract

We consider soliton solutions of the mean curvature flow, i.e., solutions which move under the mean curvature flow by a group of isometries of the ambient manifold. Several examples of solitons on manifolds are discussed. Moreover we present a local existence result for rotating solitons. We also prove global existence and stability for perturbed initial data close to a local soliton.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1321-1345.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061128

Mathematical Reviews number (MathSciNet)
MR1787070

Zentralblatt MATH identifier
0990.53068

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35K55: Nonlinear parabolic equations 35Q51: Soliton-like equations [See also 37K40]

Citation

Hungerbühler, N.; Smoczyk, K. Soliton solutions for the mean curvature flow. Differential Integral Equations 13 (2000), no. 10-12, 1321--1345. https://projecteuclid.org/euclid.die/1356061128.


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