Date(s) : 21/09/2017 iCal
15 h 30 min - 16 h 30 min
In this talk we define a class of mean curvature flows, where the curvature is replaced by its non-local conterpart, which will be introduced as well. We then introduce an appropriate Bence-Merriman-Osher (BMO) approximation scheme for the flow, showing that it is consistent even if we work in an anisotropic setting. This, together with some tools borrowed from the theory of convex bodies, allow us to show that the scheme, and thus the flow, is convexity preserving. The technique to show this latter fact, quite surprisingly, applies as well in a large class of geomtric flows. The talk is based on a joint work with A. Chambolle and M. Novaga.