Experimental Mathematics

Computation of self-similar solutions for mean curvature flow

David L. Chopp

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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.

Article information

Source
Experiment. Math. Volume 3, Issue 1 (1994), 1-15.

Dates
First available in Project Euclid: 3 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1062620999

Mathematical Reviews number (MathSciNet)
MR1302814

Zentralblatt MATH identifier
0811.53011

Subjects
Primary: 53A05: Surfaces in Euclidean space
Secondary: 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05] 65C99: None of the above, but in this section 65Y25

Citation

Chopp, David L. Computation of self-similar solutions for mean curvature flow. Experiment. Math. 3 (1994), no. 1, 1--15. https://projecteuclid.org/euclid.em/1062620999.


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