https://neckpinch.com/authors/jason-lotay/New arXiv papers by Jason Lotay, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.31343arxiv:2609.31343Fri, 25 Sep 2026 00:00:00 GMTJason D. Lotay, Goncalo Oliveira — We prove that at any nondegenerate neck pinch singularity of Lagrangian mean curvature flow of surfaces the mean curvature becomes unbounded, with control on the blow-up rate.Mean curvature flowLagrangian mean curvature flowSingularities https://arxiv.org/abs/2305.05744arxiv:2305.05744Tue, 09 May 2023 00:00:00 GMTJason D. Lotay, Goncalo Oliveira — In this article we consider the Lagrangian mean curvature flow of compact, circle-invariant, almost calibrated Lagrangian surfaces in hyperkähler 4-manifolds with circle symmetry. We show that this Lagrangian mean curvature flow can be continued for all time, through finite time singularities, and converges to a chain of special Lagrangians, thus verifying various aspects of Joyce's conjectures in this setting. We show that the singularities of the flow are neck pinches in the sense conjectured by Joyce. We also give examples where such finite time singularities are guaranteed to occur.Mean curvature flowLagrangian mean curvature flowRicci-flat & Calabi–YauSingularities4-manifoldsKähler geometry https://arxiv.org/abs/2210.12962arxiv:2210.12962Mon, 24 Oct 2022 00:00:00 GMTAaron Kennon, Jason D. Lotay — A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel G₂-structures which may also be expressed in terms of the 3-Sasakian structure. Just as Einstein metrics are critical points for the Ricci flow up to rescaling, nearly parallel G₂-structures provide natural critical points of the (rescaled) geometric flows of G₂-structures known as the Laplacian flow and Laplacian coflow. We study each of these flows in the 3-Sasakian setting and see that their behaviour is markedly different, particularly regarding the stability of the nearly parallel G₂-structures. We also compare the behaviour of the flows of G₂-structures with the (rescaled) Ricci flow.Ricci flowGeneralized & G₂ flowsEinstein metricsStability & uniquenessSasakian & contact geometry 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