https://neckpinch.com/authors/tobias-lamm/New arXiv papers by Tobias Lamm, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2109.08541/arxiv:2109.08541Fri, 17 Sep 2021 00:00:00 GMTTobias Lamm, Miles Simon — In this paper we construct solutions to Ricci DeTurck flow in four dimensions on closed manifolds which are instantaneously smooth but whose initial values g are (possibly) non-smooth Riemannian metrics whose components in smooth coordinates belong to W^(2,2) and satisfy 1/ah≤ g≤ a h for some 1<a<∞ and some smooth Riemannian metric h on M. A Ricci flow related solution is constructed whose initial value is isometric in a weak sense to the initial value of the Ricci DeTurck solution. Results for a related non-compact setting are also presented. Various L^p estimates for Ricci flow, which we require for some of the main results, are also derived. As an application we present a possible definition of scalar curvature ≥ k for W^(2,2) metrics g on closed four manifolds which are bounded in the L^(∞) sense by 1/ah≤ g≤ a h for some 1<a<∞ and some smooth Riemannian metric h on M.Ricci flow4-manifoldsScalar curvatureWeak & singular flowsBoundaries & non-compactHarmonic maps & DeTurck trick