- Experiment. Math.
- Volume 3, Issue 1 (1994), 1-15.
Computation of self-similar solutions for mean curvature flow
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.
Experiment. Math. Volume 3, Issue 1 (1994), 1-15.
First available in Project Euclid: 3 September 2003
Permanent link to this document
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.