## Asian Journal of Mathematics

### Geometric flows with rough initial data

#### Abstract

We show the existence of a global unique and analytic solution for the mean curvature flow, the surface diffusion flow and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. We also show the existence of a global unique and analytic solution to the Ricci-DeTurck flow on euclidean space for bounded initial metrics which are close to the euclidean metric in $L^\infty$ and to the harmonic map flow for initial maps whose image is contained in a small geodesic ball.

#### Article information

Source
Asian J. Math. Volume 16, Number 2 (2012), 209-235.

Dates
First available in Project Euclid: 9 April 2012