Computational and Applied Mathematics seminar

Abstract: In this talk I would like to discuss some numerical algorithms for mean curvature flow of two-dimensional surfaces through singularities. It is well known that geometric surfaces flows often undergo topological changes. For mean curvature flow this has been heavily investigated by, e.g., Hamilton, Huisken and Sinestrari, and Brendle and Huisken. Based on these works we will discuss an algorithm for mean curvature flow with numerical surgery, a process which automatically handles these topological changes, by cutting away some surface-portions and closing the remaining parts by spherical caps. In view of this, the following ethical statement seems appropriate: None of the test subjects were permanently harmed during the experiments.