Asian Journal of Mathematics

Geometric flows with rough initial data

Herbert Koch and Tobias Lamm

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1333976883

Mathematical Reviews number (MathSciNet)
MR2916362

Zentralblatt MATH identifier
1252.35159

Subjects
Primary: 35K45: Initial value problems for second-order parabolic systems 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Keywords
Geometric flows rough data local and global well-posedness

Citation

Koch, Herbert; Lamm, Tobias. Geometric flows with rough initial data. Asian J. Math. 16 (2012), no. 2, 209--235. https://projecteuclid.org/euclid.ajm/1333976883


Export citation