Computation of Self-Similar Solutions for Mean Curvature Flow
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 3 (1) , 1-15
- https://doi.org/10.1080/10586458.1994.10504572
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.Keywords
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