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


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.


Download Citation

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


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

zbMATH: 0811.53011
MathSciNet: MR1302814

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

Rights: Copyright © 1994 A K Peters, Ltd.

Vol.3 • No. 1 • 1994
Back to Top