Koch, Herbert; Lamm, Tobias Geometric flows with rough initial data. (English) Zbl 1252.35159 Asian J. Math. 16, No. 2, 209-235 (2012). The author proves the global existence and uniqueness of the analytic solution of the mean curvature flow, the surface diffusion flow and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. The author also prove the global existence and uniqueness of the analytic solution of the Ricci-DeTurck flow on Euclidean space with bounded initial metrics that is close to the Euclidean metrics in \(L^{\infty}\) norm and the harmonic map flow with initial maps whose image is contained in a small geodesic ball. Reviewer: Shu-Yu Hsu (Min-hsiung) Cited in 2 ReviewsCited in 71 Documents MSC: 35K59 Quasilinear parabolic equations 35K45 Initial value problems for second-order parabolic systems 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) Keywords:global existence; uniqueness; analytic solution; mean curvature flow; surface diffusion flow; Willmore flow; Ricci-DeTurck flow PDFBibTeX XMLCite \textit{H. Koch} and \textit{T. Lamm}, Asian J. Math. 16, No. 2, 209--235 (2012; Zbl 1252.35159) Full Text: DOI arXiv Euclid