https://neckpinch.com/authors/or-hershkovits/New arXiv papers by Or Hershkovits, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.12763arxiv:2610.12763Thu, 08 Oct 2026 00:00:00 GMTJ. M. Daniels-Holgate, Or Hershkovits, Gábor Székelyhidi — We show that for a generic compact initial surface in ℝ³, and any generic compact initial mean convex hypersurface in higher dimensions, the mean curvature flow encounters only finitely many singularities. This resolves the full generic Morse regularity conjectures of Ilmanen and Colding-Minicozzi-Pedersen in the above two cases. More generally, we show that if a mean curvature flow of a compact hypersurface has only multiplicity one spherical and cylindrical singularities, then after a small perturbation of the initial condition only non-degenerate cylindrical and spherical singularities appear.Mean curvature flowSingularities https://arxiv.org/abs/2507.16805arxiv:2507.16805Tue, 22 Jul 2025 00:00:00 GMTJ. M. Daniels-Holgate, Or Hershkovits — In this paper we demonstrate that if two mean curvature flows of compact hypersurfaces M¹ₜ and M²ₜ encounter only isolated, multiplicity one, asymptotically conical singularities at the first singular time T, and if M¹_T=M²_T then M¹ₜ=M²ₜ for every t∈ [0,T]. This is seemingly the first backwards uniqueness result for any geometric flow with singularities, that assumes neither self-shrinking nor global asymptotically conical behaviour. This necessitates the development of new global tools to deal with both the core of the singularity, its asymptotic structure, and the smooth part of the flows simultaneously. As an immediate application, we show that low entropy flows in ℝ⁴ are backwards uniqueMean curvature flowSelf-shrinkers & translatorsSingularitiesStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2503.11522arxiv:2503.11522Fri, 14 Mar 2025 00:00:00 GMTJoshua Daniels-Holgate, Or Hershkovits — Suppose (Mⁱₜ)_(t∈ [0,T)), i=1,2, are two mean curvature flows in ℝⁿ⁺¹ encountering a multiplicity one compact singularity at time T, in such a manner that for every k, the Hausdorff distance between the two flows, d_H, satisfies d_H(M¹ₜ,M²ₜ)/(T-t)^k → 0. We demonstrate that M¹ₜ=M²ₜ for every t. This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where M¹ₜ is itself a self-similarly shrinking flow.Mean curvature flowSingularities https://arxiv.org/abs/2307.11504arxiv:2307.11504Fri, 21 Jul 2023 00:00:00 GMTOr Hershkovits, Leonardo Senatore — We study mean convex mean curvature flow Mₛ of local spacelike graphs in the flat slicing of de Sitter space. We show that if the initial slice is of non-negative time and is graphical over a large enough ball, and if Mₛ is of bounded mean curvature, then as s goes to infinity, Mₛ becomes graphical in expanding balls, over which the gradient function converges to 1. In particular, if pₛ is the point lying over the center of the domain ball in Mₛ, then (Mₛ,pₛ) converges smoothly to the flat slicing of de Sitter space. This has some relation to the mean curvature flow approach to the cosmic no hair conjecture.Mean curvature flowLong-time existence & convergencePhysics https://arxiv.org/abs/2305.19137arxiv:2305.19137Tue, 30 May 2023 00:00:00 GMTKyeongsu Choi, Robert Haslhofer, Or Hershkovits — We consider the profile function of ancient ovals and of noncollapsed translators. Recall that pioneering work of Angenent-Daskalopoulos-Sesum (JDG '19, Annals '20) gives a sharp C⁰-estimate and a quadratic concavity estimate for the profile function of two-convex ancient ovals, which are crucial in their papers as well as a slew of subsequent papers on ancient solutions of mean curvature flow and Ricci flow. In this paper, we derive a sharp gradient estimate, which enhances their C⁰-estimate, and a sharp Hessian estimate, which can be viewed as converse of their quadratic concavity estimate. Motivated by our forthcoming work on ancient noncollapsed flows in ℝ⁴, we derive these estimates in the context of ancient ovals in ℝ³ and noncollapsed translators in ℝ⁴, though our methods seem to apply in other settings as well.Ricci flowMean curvature flowAncient solutionsSelf-shrinkers & translators(Non)collapsing