https://neckpinch.com/authors/alix-deruelle/New arXiv papers by Alix Deruelle, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.02164arxiv:2610.02164Thu, 01 Oct 2026 00:00:00 GMTRonan J. Conlon, Alix Deruelle — We establish the uniqueness of the soliton vector field of a complete shrinking gradient Kähler-Ricci soliton up to pushforward by biholomorphism.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniqueness https://arxiv.org/abs/2607.26054arxiv:2607.26054Tue, 28 Jul 2026 00:00:00 GMTRonan J. Conlon, Alix Deruelle — We show that any complete shrinking gradient Kähler-Ricci soliton on a resolution of a Kähler cone is necessarily asymptotically conical. From a result of Esparza, it then follows that up to pullback by biholomorphism, there exists at most one complete shrinking gradient Kähler-Ricci soliton on such a resolution. This confirms a special case of the uniqueness part of a conjecture of Song-Zhang. Some other consequences are also discussed.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniquenessBoundaries & non-compact 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/2512.18137arxiv:2512.18137Fri, 19 Dec 2025 00:00:00 GMTIvin Babu, Ronan J. Conlon, Alix Deruelle — We show that any toric asymptotically conical shrinking gradient Kähler-Ricci soliton on an anti-canonically polarised resolution of a Kähler cone satisfies a complex Monge-Ampère equation. We then set up an Aubin continuity path to solve the resulting equation and show that it has a solution at the initial value of the path parameter in the toric case. This we do by implementing another continuity method. Finally, we prove openness of the initial value of the path parameter independent of the toricity.Ricci solitonsKähler–Ricci solitonsKähler geometryBoundaries & non-compact https://arxiv.org/abs/2511.13473arxiv:2511.13473Mon, 17 Nov 2025 00:00:00 GMTAlix Deruelle, Vincent Guedj, Henri Guenancia, Ahmed Zeriahi — Given a compact Kähler manifold X and a closed, positive (1,1)-current T on X, we find sufficient conditions for T to induce a metric structure (X,d_T) which is the Gromov-Hausdorff limit of compact Kähler manifolds either in a "static" way or at time zero of smooth Kähler-Ricci flows. In dimension 1 we extend works of T. Richard and M. Simon, showing that any oriented compact Alexandrov surface with bounded integral curvature and without cusp is the initial datum of a Kähler-Ricci flow.Ricci flowKähler–Ricci flowKähler geometryWeak & singular flowsLimit spaces & RCD https://arxiv.org/abs/2410.16075arxiv:2410.16075Mon, 21 Oct 2024 00:00:00 GMTAlix Deruelle, Tristan Ozuch — In stark contrast to lower dimensions, we produce a plethora of ancient and immortal Ricci flows in real dimension 4 with Einstein orbifolds as tangent flows at infinity. For instance, for any k∈ℕ₀, we obtain continuous families of non-isometric ancient Ricci flows on \#k(S²× S²) depending on a number of parameters growing linearly in k, and a family of half-PIC ancient Ricci flows on ℂP}²\#ℂP}². The ancient/immortal dichotomy is determined by a notion of linear stability of orbifold singularities with respect to the expected way for them to appear along Ricci flow: by bubbling off Ricci-flat ALE metrics. We discuss the case of Ricci solitons orbifolds and motivate a conjecture that spherical and cylindrical solitons with orbifold singularities, which are unstable in our sense, should not appear along Ricci flow by bubbling off Ricci-flat ALE metrics.Ricci flowRicci solitonsAncient solutionsRicci-flat & Calabi–YauSingularitiesSphere theoremsStability & uniquenessLong-time existence & convergence 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/2206.10785arxiv:2206.10785Wed, 22 Jun 2022 00:00:00 GMTRichard H. Bamler, Charles Cifarelli, Ronan J. Conlon, Alix Deruelle — We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of ℂ×ℙ¹ at one point. This completes the classification of such solitons in two complex dimensions.Ricci solitonsKähler–Ricci solitonsSingularitiesSurfacesKähler geometryScalar curvature https://arxiv.org/abs/2205.08482arxiv:2205.08482Tue, 17 May 2022 00:00:00 GMTCharles Cifarelli, Ronan J. Conlon, Alix Deruelle — Let D be a toric Kähler-Einstein Fano manifold. We show that any toric shrinking gradient Kähler-Ricci soliton on certain toric blowups of ℂ× D satisfies a complex Monge-Ampère equation. We then set up an Aubin continuity path to solve this equation and show that it has a solution at the initial value of the path parameter. This we do by implementing another continuity method.Ricci solitonsKähler–Ricci solitonsEinstein metricsSingularitiesKähler geometryKähler–Einstein & K-stability 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 https://arxiv.org/abs/2203.04380arxiv:2203.04380Tue, 08 Mar 2022 00:00:00 GMTCharles Cifarelli, Ronan J. Conlon, Alix Deruelle — We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient Kähler-Ricci soliton (M, g, X) with soliton metric g with bounded scalar curvature R_g whose soliton vector field X has an integral curve along which R_gnot→0 is biholomorphic to either ℂ×ℙ¹ or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given these possibilities, we then prove a strong form of the Feldman-Ilmanen-Knopf conjecture for finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces, leading to a classification of the bubbles of such singularities in this dimension.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsSingularitiesKähler geometryScalar curvatureBoundaries & non-compact