https://neckpinch.com/authors/junsheng-zhang/New arXiv papers by Junsheng Zhang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.05643arxiv:2610.05643Mon, 05 Oct 2026 00:00:00 GMTYu Li, Junsheng Zhang — We prove a uniform scalar curvature bound, depending only on the dimension, for Kähler–Ricci shrinkers. We also prove that every noncompact Kähler–Ricci shrinker has a unique tangent cone at infinity, naturally homeomorphic to the base of its polarized Fano fibration. For shrinkers with maximal volume growth, this cone is isometric to the metric completion of the regular part equipped with the intrinsic distance induced by the limiting Kähler metric.Ricci solitonsKähler geometryScalar curvatureBoundaries & non-compactAnalytic minimal model program https://arxiv.org/abs/2610.03592arxiv:2610.03592Fri, 02 Oct 2026 00:00:00 GMTCarlos Esparza, Junsheng Zhang — For noncompact smooth Kähler-Ricci shrinkers, we prove a Matsushima theorem identifying the centralizer of the soliton field with the complexification of its Killing centralizer, uniqueness up to biholomorphism on a fixed complex manifold, and K-polystability of the associated polarized Fano fibration.Ricci solitonsKähler geometryStability & uniquenessBoundaries & non-compactKähler–Einstein & K-stabilityAnalytic minimal model program 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/2608.30779arxiv:2608.30779Mon, 31 Aug 2026 00:00:00 GMTJunsheng Zhang — In this paper, we establish several uniform estimates for Kähler–Ricci shrinkers without imposing any curvature assumptions. In particular, we prove: 1. a uniform lower bound for the entropy; 2. a uniform lower bound for the asymptotic volume ratio of Kähler–shrinkers with maximal volume growth; 3. a uniform lower bound for the scalar curvature on balls centered at a minimum point of the soliton potential for non-Gaussian shrinkers.Ricci solitonsKähler geometryScalar curvature https://arxiv.org/abs/2607.25644arxiv:2607.25644Tue, 28 Jul 2026 00:00:00 GMTYu Li, Junsheng Zhang — We study the metric geometry of finite-time singularities of volume-noncollapsed Kähler-Ricci flows and the geometry at infinity of Ricci shrinkers. For a compact volume-noncollapsed Kähler-Ricci flow approaching its first singular time, we prove that the time slices converge to a unique Gromov-Hausdorff limit, canonically identified with the time-zero slice of the Ricci-flow spacetime completion. Its regular part is identified with the complement of the null locus, and we show that the singular set has Hausdorff codimension at least four. For Kähler-Ricci shrinkers, we relate the geometry at infinity to the associated Fano fibration. We prove local smooth convergence to a Kähler cone metric on the locus where the fibration is biholomorphic, and characterize asymptotic conicality by biholomorphicity outside a compact set. For Ricci shrinkers with bounded scalar curvature, we show that local compactness of the time-zero slice implies pointed Gromov-Hausdorff convergence of the full self-similar flow to that slice. As applications, we prove uniqueness of the tangent space at infinity for Kähler-Ricci shrinkers with bounded scalar curvature and Euclidean volume growth whose soliton vector field generates an S¹-action, and for all four-dimensional Ricci shrinkers with bounded scalar curvature.Ricci flowKähler–Ricci flowRicci solitonsSingularities(Non)collapsing4-manifoldsKähler geometryScalar curvatureLimit spaces & RCDStability & uniqueness https://arxiv.org/abs/2605.25213arxiv:2605.25213Sun, 24 May 2026 00:00:00 GMTMax Hallgren, Junsheng Zhang — We prove that any singular Kähler–Ricci shrinker X arising as a noncollapsed limit of Kähler–Ricci flows admits a natural structure of a polarized Fano fibration. We also show that it is simply connected, has unique tangent cones at every point, and is a smooth orbifold outside a subset of complex codimension at least three. As an application, we prove a new long-time pseudolocality theorem for almost-selfsimilar Kähler–Ricci flows.Ricci flowKähler–Ricci flowRicci solitons(Non)collapsingKähler geometryAnalytic minimal model program https://arxiv.org/abs/2602.19913arxiv:2602.19913Mon, 23 Feb 2026 00:00:00 GMTMan-Chun Lee, Valentino Tosatti, Junsheng Zhang — We show that the normalized Kähler-Ricci flow on a compact Kähler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted Kähler-Einstein metric on the canonical model, as conjectured by Song-Tian's analytic mimimal model program.Ricci flowKähler–Ricci flowEinstein metricsKähler geometryLimit spaces & RCDLong-time existence & convergenceKähler–Einstein & K-stabilityAnalytic minimal model program https://arxiv.org/abs/2511.14735arxiv:2511.14735Tue, 18 Nov 2025 00:00:00 GMTJunsheng Zhang — We prove a weaker version of the transcendental base-point freeness on compact Kähler manifolds. As a consequence, we derive the diameter lower bound for finite time singularities of Kähler-Ricci flow with non-Fano initial data.Ricci flowKähler–Ricci flowSingularitiesKähler geometry https://arxiv.org/abs/2410.09661arxiv:2410.09661Sat, 12 Oct 2024 00:00:00 GMTSong Sun, Junsheng Zhang — In this paper, we build connections between Kähler-Ricci shrinkers, i.e., complete (possibly non-compact) shrinking gradient Kähler-Ricci solitons, and algebraic geometry. In particular, we (1). prove that a Kähler-Ricci shrinker is naturally a quasi-projective variety, using birational algebraic geometry; (2). formulate a conjecture relating the existence of Kähler-Ricci shrinkers and K-stability of polarized Fano fibrations, which unifies and extends the YTD type conjectures for Kähler-Einstein metrics, Ricci-flat Kähler cone metrics and compact Kähler-Ricci shrinkers; (3). formulate conjectures connecting tangent flows at singularities of Kähler-Ricci flows and algebraic geometry, via a 2-step degeneration for the weighted volume of a Fano fibration.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsEinstein metricsRicci-flat & Calabi–YauSingularitiesKähler geometryStability & uniquenessBoundaries & non-compact