https://neckpinch.com/authors/otis-chodosh/New arXiv papers by Otis Chodosh, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2502.09727arxiv:2502.09727Thu, 13 Feb 2025 00:00:00 GMTOtis Chodosh, Yi Lai, Kai Xu — We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be ℝ³. We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar curvature and bounded geometry. Our results rely on the maximal weak solution to inverse mean curvature flow due to the third-named author.Mean curvature flowOther curvature flowsInverse mean curvature flow3-manifoldsScalar curvatureWeak & singular flows https://arxiv.org/abs/2409.01463arxiv:2409.01463Mon, 02 Sep 2024 00:00:00 GMTOtis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze — Bamler–Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R^3 and combined it with the authors' work on generic mean curvature flows to fully resolve Huisken's genericity conjecture. In this paper we show that a short density-drop theorem plus the Bamler–Kleiner multiplicity-one theorem for tangent flows at the first nongeneric singular time suffice to resolve Huisken's conjecture – without relying on the strict genus drop theorem for one-sided ancient flows previously established by the authors.Mean curvature flowAncient solutionsSingularities https://arxiv.org/abs/2312.00759arxiv:2312.00759Fri, 01 Dec 2023 00:00:00 GMTOtis Chodosh, J. M. Daniels-Holgate, Felix Schulze — We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface Mⁿ⊂ ℝⁿ⁺¹, 2≤ n≤ 6, with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens.Mean curvature flowSingularitiesWeak & singular flowsBoundaries & non-compact https://arxiv.org/abs/2309.03856arxiv:2309.03856Thu, 07 Sep 2023 00:00:00 GMTOtis Chodosh, Christos Mantoulidis, Felix Schulze — We prove that the mean curvature flow of a generic closed embedded hypersurface in ℝ⁴ or ℝ⁵ with entropy ≤ 2, or with entropy ≤ λ(S¹) if in ℝ⁶, encounters only generic singularities.Mean curvature flowSingularities https://arxiv.org/abs/2302.08409arxiv:2302.08409Thu, 16 Feb 2023 00:00:00 GMTOtis Chodosh, Kyeongsu Choi, Felix Schulze — We show that the mean curvature flow of a generic closed surface in ℝ³ avoids multiplicity one tangent flows that are not round spheres/cylinders. In particular, we show that any non-cylindrical self-shrinker with a cylindrical end cannot arise generically.Mean curvature flowSelf-shrinkers & translatorsSingularities