##### Department of Mathematics,

University of California San Diego

****************************

### Math 258 - Differential Geometry

## Nick Edelen

#### Northwestern

## Existence and partial regularity of the free-boundary mean curvature flow

##### Abstract:

A surface has geometric free-boundary in a barrier hypersurface if its boundary meets the barrier orthogonally, like a bubble on a bathtub. We extend Brakke's weak notion of mean curvature flow to have a free-boundary condition, and using toy examples we show why this extension is necessary. Contrary to the classical flow, for which the barrier is ``invisible,'' the weak flow allows for the surfaces to ``pop'' upon tangential contact with the barrier. When the initial surface is mean-convex, we generalize White's partial regularity and structure theory to the free-boundary setting. This is in part joint work with Robert Haslhofer, Mohammad Ivaki, and Jonathan Zhu.

Hosts: Luca Spolaor and Lei Ni

### January 8, 2020

### 10:00 AM

### AP&M 6402

****************************