Geometric flows with rough initial data

Herbert Koch; Tobias Lamm

Geometric flows with rough initial data

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arxiv 0902.1488 v2 pith:6TGOLSXK submitted 2009-02-09 math.DG math.AP

Herbert Koch , Tobias Lamm This is my paper · ORCID

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keywords flowinitialanalyticdataeuclideanexistencegloballipschitz

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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.

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Well-posedness for the mean curvature flow on the half-space and on bounded domains
math.AP 2026-08 conditional novelty 6.0 of 10

Graphical mean curvature flow with zero boundary data is locally well-posed for approximable Lipschitz graphs, globally well-posed for small initial slopes, and decays exponentially on bounded domains.

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