# Geometric Analysis and Topology Seminar

#### On the Regularity of Varifold Mean Curvature Flow

**Speaker:**
Yoshihiro Tonegawa, Hokkaido University

**Location:**
Warren Weaver Hall 517

**Date:**
Tuesday, February 11, 2014, 11 a.m.

**Synopsis:**

In his well-known book published in 1978, Brakke initiated the theory of mean curvature flow (MCF) using the notion of varifold and studied the existence and regularity properties. While there have been many advances in the understanding on his version of MCF, the full proof of his regularity theorem remained out of reach even for specialists of MCF. Recently we gave a new and complete proof of Brakke's regularity theorem which also comes with a natural generalization. The generalization fits well with its stationary counterpart, Allard's regularity theorem, and is useful to prove the partial regularity of Brakke's MCF in general Riemannian manifolds. Starting from the definition, I will explain the outline of the proof of the regularity theorem.