https://neckpinch.com/authors/maximilian-moser/New arXiv papers by Maximilian Moser, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2410.08596/arxiv:2410.08596Fri, 11 Oct 2024 00:00:00 GMTHelmut Abels, Christoph Hurm, Maximilian Moser — We prove convergence of the nonlocal Allen-Cahn equation to mean curvature flow in the sharp interface limit, in the situation when the parameter corresponding to the kernel goes to zero fast enough with respect to the diffuse interface thickness. The analysis is done in the case of a W^(1,1)-kernel, under periodic boundary conditions and in both two and three space dimensions. We use the approximate solution and spectral estimate from the local case, and combine the latter with an L²-estimate for the difference of the nonlocal operator and the negative Laplacian from Abels, Hurm arXiv:2307.02264. To this end, we prove a nonlocal Ehrling-type inequality to show uniform H³-estimates for the nonlocal solutions.Mean curvature flowBoundaries & non-compactEigenvalues & spectrumPhase fields & multiphase flows https://neckpinch.com/papers/2404.02884/arxiv:2404.02884Wed, 03 Apr 2024 00:00:00 GMTJulian Fischer, Sebastian Hensel, Alice Marveggio, Maximilian Moser — We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes.Mean curvature flowWeak & singular flowsStability & uniquenessPhase fields & multiphase flows