https://neckpinch.com/authors/charles-cifarelli/New arXiv papers by Charles Cifarelli, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.16733arxiv:2609.16733Tue, 15 Sep 2026 00:00:00 GMTCharles Cifarelli, Ronan Conlon, Max Hallgren, Junsheng Zhang — For any volume-collapsing finite-time singularity of a Kähler-Ricci flow on a compact Kähler surface, we show the flow satisfies a Type I curvature bound and classify the corresponding tangent flows. Combined with previous results, this shows that any finite-time singularity of a Kähler-Ricci flow on a compact Kähler surface is of Type I.Ricci flowKähler–Ricci flowSingularities(Non)collapsingKähler geometry https://arxiv.org/abs/2512.03323arxiv:2512.03323Wed, 03 Dec 2025 00:00:00 GMTCharles Cifarelli, Carlos Esparza — Recently, Sun-Zhang have developed an algebraic theory for Kähler-Ricci shrinkers showing that they admit the structure of a polarized Fano fibration (π: X → Y, ξ). In particular, they conjecture that existence of a Kähler-Ricci shrinker metric is equivalent to a notion of K-stability. We prove one direction of this conjecture, namely that existence of a Kähler-Ricci shrinker metric g implies K-polystability of (π: X → Y, ξ), in the case that the Ricci curvature of g decays at infinity. As an application, we give a non-existence result: if M is the blowup of a six-dimensional quadric along a two-dimensional subquadric, then the total space X of the cube root of K_M is a polarized Fano fibration not admitting a Kähler-Ricci shrinker.Ricci solitonsSingularitiesSurfacesKähler geometryStability & uniquenessBoundaries & non-compactKähler–Einstein & K-stabilityAnalytic minimal model program https://arxiv.org/abs/2410.23645arxiv:2410.23645Thu, 31 Oct 2024 00:00:00 GMTCharles Cifarelli — Let B be a Kähler-Einstein Fano manifold, and L → B be a suitable root of the canonical bundle. We give a construction of complete Calabi-Yau metrics and gradient shrinking, steady, and expanding Kähler-Ricci solitons on the total space M, rm dim_ℂ M = n of certain vector bundles E → B, composed of direct sums of powers of L. We employ the theory of hamiltonian 2-forms [2, 3] as an Ansatz, thus generalizing recent work of the author and Apostolov on ℂⁿ [5], as well as that of Cao, Koiso, Feldman-Ilmanen-Knopf, Futaki-Wang, and Chi Li [10, 26, 23, 24, 30] when E has Calabi symmetry. As a result, we obtain new examples of asymptotically conical Kähler shrinkers, Calabi-Yau metrics with ALF-like volume growth, and steady solitons with volume growth R^((4n-2)/3).Ricci solitonsKähler–Ricci solitonsEinstein metricsRicci-flat & Calabi–YauKähler geometryBoundaries & non-compactKähler–Einstein & K-stability https://arxiv.org/abs/2305.15626arxiv:2305.15626Thu, 25 May 2023 00:00:00 GMTVestislav Apostolov, Charles Cifarelli — For each partition of the positive integer n= ℓ +∑ⱼ₌₁^ℓ dⱼ, where ℓ≥ 1 and dⱼ ≥ 0 are integers, we construct a continuous (ℓ−1)-parameter family of explicit complete gradient steady Kähler–Ricci solitons on ℂⁿ admitting a hamiltonian 2-form of order ℓ and symmetry group rm U(d₁+ 1) × ⋯ × rm U(d_ℓ + 1). For ℓ=1, d₁=n-1 we obtain Cao's example [17] whereas for other partitions the metrics are new. Furthermore, when n=2, ℓ=2, d₁=d₂=0 we obtain complete gradient steady Kähler–Ricci solitons on ℂ² which have positive sectional curvature but are not isometric to Cao's rm U(2)-invariant example. This disproves a conjecture by Cao. We also present a construction yielding explicit families of complete gradient steady Kähler-Ricci solitons on ℂⁿ containing higher dimensional extensions of the Taub-NUT Ricci-flat Kähler metric on ℂ². When n≥ 3, the complete Ricci-flat Kähler metrics, and when n≥ 2, their deformations to complete gradient steady Kähler Ricci solitons seem not to have been observed before our work.Ricci solitonsKähler–Ricci solitonsRicci-flat & Calabi–YauSphere theoremsKähler geometry https://arxiv.org/abs/2303.03263arxiv:2303.03263Mon, 06 Mar 2023 00:00:00 GMTCharles Cifarelli — We study the weighted constant scalar curvature, a modified scalar curvature introduced by Lahdili depending on weight functions (v, w), on certain non-compact semisimple toric fibrations, a generalization of the Calabi Ansatz defined by Apostolov–Calderbank–Gauduchon–Tønnesen-Friedman. We show that the natural analog of the weighted Futaki invariant of Lahdili can under reasonable assumptions be interpreted on an unbounded polyhedron P ⊂ ℝⁿ associated to M. In particular, we fix a certain class 𝓦 of weights (v, w), and prove that if M admits a weighted cscK metric, then P is K-stable, and we give examples of weights on ℂ² for which the weighted Futaki invariant vanishes but do not admit (v, w)-cscK metrics. Following Jubert, we introduce a weighted Mabuchi energy 𝓜_(v,w) and show that the existence of a (v, w)-cscK metric implies that it 𝓜_(v,w) proper, and prove a uniqueness result using the method of Guan. We show that weighted K-stability of the abstract fiber ℂ is sufficient for the existence of weighted cscK metrics on the total space of line bundles L → B over a compact Kähler base, extending a result of Lahdili in the ℙ¹-bundles case. The right choice of weights corresponds to the (shrinking) Kähler-Ricci soliton equation, and we give an interpretation of the asyptotic geometry in this case.Ricci solitonsKähler–Ricci solitonsKähler geometryScalar curvatureStability & uniquenessBoundaries & non-compactKähler–Einstein & K-stability 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/2203.04380arxiv: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