https://neckpinch.com/authors/felix-schulze/New arXiv papers by Felix Schulze, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.18687arxiv:2609.18687Wed, 16 Sep 2026 00:00:00 GMTRichard H. Bamler, Felix Schulze, Lu Wang — We show that a compact mean curvature flow whose singularities have multiplicity-one cylindrical tangent flows admits a smooth Morse resolution. The resolution agrees with the spacetime track outside any prescribed neighborhood of its singular set and all its critical points have the expected index. No nondegeneracy or isolatedness assumption is required. In the mean-convex case the result follows by smoothing the global arrival function.Mean curvature flowSingularities https://arxiv.org/abs/2603.22086arxiv:2603.22086Mon, 23 Mar 2026 00:00:00 GMTAlix Deruelle, Man-Chun Lee, Felix Schulze, Miles Simon, Peter M. Topping — Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all dimensions. In order to do so we develop a lifting technique that allows us to handle manifolds that are collapsed at infinity. This new method also gives an alternative way of handling collapsed manifolds in the known three-dimensional case. As part of this approach, we prove a Ricci flow curvature estimate of a type that would normally be derived from the Harnack inequality, but without requiring the strong curvature positivity hypothesis demanded by Harnack. We give an improved gap theorem as a further application.Ricci flowHarnack inequalitiesCurvature pinching3-manifoldsSphere theoremsBoundaries & non-compact 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/2403.00708arxiv:2403.00708Fri, 01 Mar 2024 00:00:00 GMTAlix Deruelle, Felix Schulze, Miles Simon — We study n-dimensional Ricci flows with non-negative Ricci curvature where the curvature is pointwise controlled by the scalar curvature and bounded by C/t, starting at metric cones which are Reifenberg outside the tip. We show that any such flow behaves like a self-similar solution up to an exponential error in time. As an application, we show that smooth n-dimensional complete non-compact Riemannian manifolds which are uniformly PIC1-pinched, with positive asymptotic volume ratio, are Euclidean. This confirms a higher dimensional version of a conjecture of Hamilton and Lott under the assumption of non-collapsing. It also yields a new and more direct proof of the original conjecture of Hamilton and Lott in three dimensions.Ricci flow(Non)collapsingSphere theoremsScalar curvatureWeak & singular flowsBoundaries & non-compact 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 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 https://arxiv.org/abs/2203.15313arxiv:2203.15313Tue, 29 Mar 2022 00:00:00 GMTAlix Deruelle, Felix Schulze, Miles Simon — This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from below and whose curvature is bounded by c· t⁻¹ converge to one another at an exponential rate once they have been appropriately gauged. As an application, we show that smooth three dimensional, complete, uniformly Ricci-pinched Riemannian manifolds with bounded curvature are either compact or flat, thus confirming a conjecture of Hamilton and Lott.Ricci flow3-manifoldsWeak & singular flowsStability & uniqueness