https://neckpinch.com/authors/florian-litzinger/New arXiv papers by Florian Litzinger, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2606.23272/arxiv:2606.23272Mon, 22 Jun 2026 00:00:00 GMTMan-Chun Lee, Florian Litzinger, Miles Simon — In this work, we study the positive mass theorem under critical low regularity assumptions using Ricci flow smoothing. We show that asymptotically flat manifolds (Mⁿ,g) of regularity L^∞∩ W^(1,n) with non-negative distributional scalar curvature have non-negative ADM mass. Furthermore, when the ADM mass vanishes, the manifold is globally isometric to Euclidean space with respect to an integral distance introduced by De Cecco-Palmieri. This extends the recent work of Hafemann to the critical regularity case. Our approach is based on showing that Riemannian metrics of regularity L^∞∩ W^(1,n), whose scalar curvature is bounded from below in the distributional sense, admit a Ricci flow smoothing whose scalar curvature is bounded from below by the same initial lower bound in the classical sense. In contrast, Cecchini-Frenck-Zeidler constructed examples of metrics which are in L^∞∩ W^(1,p) for all 2<p<n, and whose distributional scalar curvature is bounded from below, that cannot be approximated by smooth metrics with the same scalar curvature lower bound. In this sense, our result is optimal.Ricci flowScalar curvatureBoundaries & non-compactPhysics https://neckpinch.com/papers/2304.02487/arxiv:2304.02487Wed, 05 Apr 2023 00:00:00 GMTFlorian Litzinger — We consider curve shortening flow of arbitrary codimension in an Euclidean background. We show that, close to a singularity, the flow is asymptotically planar, paralleling Altschuler's work in the case of space curves, and analyse the blow-up limits of the flow. Using these results, we then prove that the curve shortening flow of initial curves with an entropy bound converges to a round point in finite time.Curve shorteningSingularities