https://neckpinch.com/authors/tobias-marxen/New arXiv papers by Tobias Marxen, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2002.06586/arxiv:2002.06586Sun, 16 Feb 2020 00:00:00 GMTKlaus Kroencke, Tobias Marxen, Boris Vertman — In this paper we consider a Ricci de Turck flow of spaces with isolated conical singularities, which preserves the conical structure along the flow. We establish that a given initial regularity of Ricci curvature is preserved along the flow. Moreover under additional assumptions, positivity of scalar curvature is preserved under such a flow, mirroring the standard property of Ricci flow on compact manifolds. The analytic difficulty is the a priori low regularity of scalar curvature at the conical tip along the flow, so that the maximum principle does not apply. We view this work as a first step toward studying positivity of the curvature operator along the singular Ricci flow.Ricci flowSingularitiesScalar curvatureWeak & singular flowsHarmonic maps & DeTurck trick https://neckpinch.com/papers/1903.03502/arxiv:1903.03502Fri, 08 Mar 2019 00:00:00 GMTKlaus Kroencke, Oliver Lindblad Petersen, Felix Lubbe, Tobias Marxen, Wolfgang Maurer, Wolfgang Meiser, Oliver C. Schnürer, Áron Szabó, Boris Vertman — We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold M×ℝ, where M is asymptotically flat. If the initial hypersurface F₀⊂ M×ℝ is uniformly spacelike and asymptotic to M×s\ for some s∈ℝ at infinity, we show that a mean curvature flow starting at F₀ exists for all times and converges uniformly to M×s\ as t→ ∞.Mean curvature flowBoundaries & non-compactLong-time existence & convergencePhysics