# Analysis Seminar

#### Eventual regularization for fractional mean curvature flow

Speaker: Stephen Cameron, CIMS

Location: Warren Weaver Hall 1302

Date: Thursday, October 24, 2019, 11 a.m.

Synopsis:

The $s$-perimeter of a set $E$ is given by the $\dot{W}^{s,1}$ norm of its characteristic function for $s\in (0,1)$.
The first variation of this functional gives the $s$-mean curvature $H_s$, the fractional, nonlocal analog of typical mean curvature.  We
show that if your initial surface is bounded between two hyperplanes, then after evolving for a fixed finite time under fractional mean
curvature flow the surface becomes a Lipschitz graph.  The proof is inherently nonlocal in nature, and in fact the theorem is false for
classical mean curvature flow.