Experimental Mathematics

Computation of self-similar solutions for mean curvature flow

David L. Chopp

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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

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

First available in Project Euclid: 3 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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