Geometric flows with rough initial data

Date
Authors
Koch, Herbert
Lamm, Tobias
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
Comment: Minor corrections, added a result for the surface diffusion flow
Keywords
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs
Citation
Collections