Asian Journal of Mathematics
Volume 16 (2012)
Geometric flows with rough initial data
Pages: 209 – 235
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.
Geometric flows; rough data; local and global well-posedness
2010 Mathematics Subject Classification