# UBC Mathematics Colloquium

## Albert Chau

(UBC)

## Lagrangian Mean Curvature flow for entire Lipschitz graphs

### Fri., Sept. 25, 2009, 3:00pm, MATX 1100

In this talk I will give a brief introduction to the mean

curvature flow and review some classic theory and results in the
area. I

will then introduce the Lagrangian mean curvature flow and discuss
recent

results which can be viewed as Lagrangian versions of classic results of

Ecker-Huisken on the mean curvature flow of entire hypersurfaces.
In

particular, we prove existence of longtime smooth solutions to mean

curvature flow of entire Lipschitz Lagrangian graphs. As an
application of

our estimates we classify all self-similar entire solutions to
Lagrangian

mean curvautre flow satisfying certain conditions. The results are from

joint work with Jingyi Chen and Weiyong He.