https://neckpinch.com/authors/gabor-szekelyhidi/New arXiv papers by Gábor Székelyhidi, 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/2606.00964arxiv:2606.00964Sun, 31 May 2026 00:00:00 GMTGábor Székelyhidi — We construct a mean curvature flow with surgery starting with any compact mean convex hypersurface in ℝⁿ⁺¹, extending previous results of Huisken-Sinestrari, Brendle-Huisken, and Haslhofer-Kleiner for 2-convex flows. In contrast with previous constructions of mean curvature flow with surgery, the topological surgeries are performed by the flow itself through nondegenerate cylindrical singularities. At the same time the flow needs to be slightly adjusted at finitely many smooth times.Mean curvature flowSingularitiesSurgery https://arxiv.org/abs/2603.11022arxiv:2603.11022Wed, 11 Mar 2026 00:00:00 GMTGábor Székelyhidi — We show that for generic smooth compact initial surfaces the mean curvature flow in ℝ³ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in ℝ³.Mean curvature flowSingularitiesSurgery https://arxiv.org/abs/2602.15771arxiv:2602.15771Tue, 17 Feb 2026 00:00:00 GMTGábor Székelyhidi — We introduce a notion of nondegenerate neck pinch singularity along the Lagrangian mean curvature flow of surfaces in a Calabi-Yau surface. We show that such singularities can occur, are stable under small perturbations, and any neck pinch singularity can be perturbed to such a nondegenerate singularity near the singular time. Using this we answer some questions raised by Neves and Joyce. We also introduce nondegenerate teardrop singularities and show that these cannot occur for embedded flows.Mean curvature flowLagrangian mean curvature flowRicci-flat & Calabi–YauSingularitiesKähler geometry https://arxiv.org/abs/2505.01943arxiv:2505.01943Sat, 03 May 2025 00:00:00 GMTMax Hallgren, Gábor Székelyhidi — We study two different natural notions of singular Kähler-Einstein metrics on normal complex varieties. In the setting of singular Ricci flat Kähler cone metrics that arise as non-collapsed limits of sequences of Kähler-Einstein metrics or Kähler-Ricci flows, we show that an a priori weaker notion is equivalent to the stronger one introduced by Eyssidieux-Guedj-Zeriahi, and in particular the underlying variety has log terminal singularities in this case. Our method applies to more general singular Kähler-Einstein spaces as well, assuming that they define RCD spaces.Ricci flowKähler–Ricci flowEinstein metricsRicci-flat & Calabi–YauSingularities(Non)collapsingKähler geometryWeak & singular flowsLimit spaces & RCDKähler–Einstein & K-stability https://arxiv.org/abs/2502.09825arxiv:2502.09825Thu, 13 Feb 2025 00:00:00 GMTYifan Chen, Shih-Kai Chiu, Max Hallgren, Gábor Székelyhidi, Tat Dat Tô, Freid Tong — We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kähler currents. In particular the result applies to singular Kähler-Einstein metrics on klt pairs, and an analogous result holds for Kähler-Ricci solitons. In addition we show that if a singular Kähler-Einstein metric can be approximated by smooth metrics on a resolution whose Ricci curvature has negative part that is bounded uniformly in L^p for p > (2n-1)/n, then the metric defines an RCD space.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryLimit spaces & RCDKähler–Einstein & K-stabilityAnalytic minimal model program https://arxiv.org/abs/2410.22172arxiv:2410.22172Tue, 29 Oct 2024 00:00:00 GMTYang Li, Gábor Székelyhidi — We study singularities along the Lagrangian mean curvature flow with tangent flows given by multiplicity one special Lagrangian cones that are smooth away from the origin. Some results are: uniqueness of all such tangent flows in dimension two; uniqueness in any dimension when the link of the cone is connected; the existence of nontrivial special Lagrangian blowup limits. We also prove a singular version of Imagi-Joyce-dos Santos's uniqueness result of the Lawlor neck. As an application we prove that in any dimension, singularities that admit a tangent flow given by the union of two transverse planes is modeled on shrinking Lawlor necks at suitable scales.Mean curvature flowLagrangian mean curvature flowSingularitiesStability & uniqueness https://arxiv.org/abs/2208.11054arxiv:2208.11054Tue, 23 Aug 2022 00:00:00 GMTJason D. Lotay, Felix Schulze, Gábor Székelyhidi — Let Lₜ be a zero Maslov, rational Lagrangian mean curvature flow in a compact Calabi-Yau surface, and suppose that at the first singular time a tangent flow is given by the static union of two transverse planes. We show that in this case the tangent flow is unique, and that the flow can be continued past the singularity as an immersed, smooth, zero Maslov, rational Lagrangian mean curvature flow. Furthermore, if L₀ is a sphere that is stable in the sense of Thomas-Yau, then such a singularity cannot form.Mean curvature flowLagrangian mean curvature flowRicci-flat & Calabi–YauSingularitiesKähler geometryWeak & singular flows https://arxiv.org/abs/2204.13836arxiv:2204.13836Fri, 29 Apr 2022 00:00:00 GMTJason D. Lotay, Felix Schulze, Gábor Székelyhidi — Suppose that 𝓜 is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in ℂⁿ. We show that if 𝓜 has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then 𝓜 is a translator. In particular in ℂ², all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators.Mean curvature flowLagrangian mean curvature flowAncient solutionsSelf-shrinkers & translators