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1994 Computation of self-similar solutions for mean curvature flow
David L. Chopp
Experiment. Math. 3(1): 1-15 (1994).

Abstract

We describe a numerical algorithm to compute surfaces that are approximately self-similar under mean curvature flow. The method restricts computation to a two-dimensional subspace of the space of embedded manifolds that is likely to contain a self-similar solution.

Using the algorithm, we recover the self-similar torus of Angenent and find several surfaces that appear to approximate previously unknown self-similar surfaces. Two of them may prove to be counterexamples to the conjecture of uniqueness of the weak solution for mean curvature flow for surfaces.

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David L. Chopp. "Computation of self-similar solutions for mean curvature flow." Experiment. Math. 3 (1) 1 - 15, 1994.

Information

Published: 1994
First available in Project Euclid: 3 September 2003

zbMATH: 0811.53011
MathSciNet: MR1302814

Subjects:
Primary: 53A05
Secondary: 58E12 , 65C99 , 65Y25

Rights: Copyright © 1994 A K Peters, Ltd.

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Vol.3 • No. 1 • 1994
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