https://neckpinch.com/authors/alexander-mramor/New arXiv papers by Alexander Mramor, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.28337arxiv:2609.28337Wed, 23 Sep 2026 00:00:00 GMTAlexander Mramor — In this work we study the long term behavior of the curve shortening flow of asymptotically conical curves with convex projections in ℝ³.Curve shorteningBoundaries & non-compact https://arxiv.org/abs/2509.26515arxiv:2509.26515Tue, 30 Sep 2025 00:00:00 GMTAlexander Mramor, Louis Yudowitz — We construct an embedded ancient solution to the mean curvature flow which is qualitatively given by a "stack" of two ancient pancakes joined by a neck. Our solution is closed, non-convex, and contained in a slab.Mean curvature flowAncient solutions https://arxiv.org/abs/2412.03475arxiv:2412.03475Wed, 04 Dec 2024 00:00:00 GMTAlexander Mramor, Ao Sun — In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with multiplicity. Using a perturbative argument then we construct piecewise almost regular flows which either go extinct in finite time or flow to a stable minimal surface, possibly with multiplicity. We apply these results to construct minimal surfaces in 3-manifolds in a variety of circumstances, mainly novel from the point of the view that the arguments are via parabolic methods.Mean curvature flowSingularities3-manifoldsMinimal & CMC surfaces https://arxiv.org/abs/2201.02134arxiv:2201.02134Thu, 06 Jan 2022 00:00:00 GMTTheodora Bourni, Alexander Mramor — In this note we construct new nonplanar ancient (in fact, eternal) solutions to the curve shortening flow in ℝ³, built out of translating grim reapers laying in perpendicular planes.Curve shorteningAncient solutionsSelf-shrinkers & translators