Tim Laux (University of Berkeley): A gradient-flow approach to thresholding for codimension-two mean-curvature flow
Wednesday, 10.01.2018 16:00 im Raum M5
The thresholding scheme is an efficient numerical scheme for mean curvature flow with natural extensions to mutliphase systems as well as higher codimensions. In this talk I will present the first convergence proof for the scheme in codimension two.
It is well-known that for hypersurfaces, the scheme is compatible with the gradient-flow structure of mean-curvature flow in the sense that it satisfies a minimizing movements principle (Esedoglu-Otto ?15). I will show that an analogous principle holds true for thresholding in codimension two. In particular, the scheme dissipates an energy reminiscent of the Ginzburg-Landau energy of a vortex filament. The main ingredient for the (short-time) convergence result is a sharp energy bound away from the smooth mean-curvature flow. As opposed to previous results on hypersurfaces (L.-Otto ?16, ?17), this result is unconditional. If time permits, I will demonstrate how this variational viewpoint facilities the design of new schemes.
This is joint work with Aaron Yip (Purdue).