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Analysis of the thresholding scheme for mean curvature flow in codimension two

Date: Thursday, January 10, 2019 10:00 - 11:00
Speaker: Tim Laux (Berkeley)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Julian Fischer
Contact: SORONDA Marija
Lab building west seminar room

Abstract:

The thresholding scheme, also known as diffusion generated motion, is an efficient numerical algorithm for computing mean curvature flow (MCF). In this talk I will briefly discuss the case of hypersurfaces, and then present our first convergence analysis in the case of codimension two. The proof is based on a new generalization of the minimizing movements interpretation for hypersurfaces (Esedoglu-Otto '15) by means of an energy that approximates the Dirichlet energy of the state function. As long as a smooth MCF exists, we establish uniform energy estimates for the approximations away from the smooth solution and prove convergence towards this MCF. The result relies in a very crucial manner on a new sharp monotonicity formula for the thresholding energy. This is joint work with Aaron Yip (Purdue).
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