https://neckpinch.com/topics/kahler-geometry/New arXiv papers on kähler geometry, from Neckpinch Wed, 04 Nov 2026 13:15:59 GMT https://neckpinch.com/papers/2611.01968/arxiv:2611.01968Sun, 01 Nov 2026 00:00:00 GMTHaozhao Li, Bing Wang, Kai Zheng — We study global smooth Calabi flows on polarized Kähler surfaces (M,L), assuming uniformly bounded Sobolev constants and the algebraic conditions χ(𝓞_M)=1 and c₁(M)· c₁(L)>0. Using the orbifold compactness theorem, we prove a uniform Bergman estimate, construct a normal test configuration for each geometric limit, and establish uniqueness of the extremal orbifold limit up to polarized holomorphic isometry. K-polystability then identifies the limit with the original surface and gives a constant scalar curvature Kähler metric. We also prove finite-group equivariant versions of these results. Independently of the flow, we obtain a uniform Bergman lower bound for polarized cscK surfaces with bounded volume and Sobolev constants and |S|≤1. We illustrate the hypotheses with nonstationary flows near a product cscK metric on ℙ¹×ℙ¹ and near Calabi's non-cscK extremal metric on the first Hirzebruch surface. Their controlled-cone energy inequalities follow from elementary calculations and continuity.Other curvature flowsKähler geometryScalar curvatureLimit spaces & RCDStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/2611.01882/arxiv:2611.01882Sun, 01 Nov 2026 00:00:00 GMTHaozhao Li, Bing Wang, Kai Zheng — We study global Calabi flows g(t) on compact Kähler surfaces with a uniform Sobolev constant. For any sequence tⱼ→∞, set gⱼ(t):=g(tⱼ+t). After passing to a subsequence, these flows converge to an eternal Calabi flow on a compact extremal Kähler orbifold surface. The convergence holds in the spacetime hat C^∞-Cheeger–Gromov topology: it is uniform in the Gromov–Hausdorff sense on compact time intervals and smooth away from the orbifold singularities, using comparisons fixed in time.Other curvature flowsSingularitiesKähler geometryLimit spaces & RCDKähler–Einstein & K-stability https://neckpinch.com/papers/2611.01623/arxiv:2611.01623Sun, 01 Nov 2026 00:00:00 GMTHongyu Chen, Li Ma, Li Sheng — On every unit-volume flat complex three-torus, we construct a solution of the volume-preserving conformal Chern–Calabi flow with a finite-time Chern Type-I singularity at any prescribed point. The full spatial supremum has an exact asymptotic coefficient, and prescribed rescalings converge to a complete nonflat radial shrinking solution. The positive part of Chern scalar curvature can remain arbitrarily small throughout the flow, as can each prescribed subcritical spatial curvature norm. We determine the punctured terminal metric, its one-point completion and unique nonflat tangent cone, and the terminal energy asymptotics. We also exclude Chern Type-II under a logarithmically improved critical weak L³ bound on Chern scalar curvature, and prove a separate scale-invariant integral criterion involving first Chern–Ricci curvature. The constructed singular solutions satisfy both criteria.Other curvature flowsSingularitiesKähler geometryScalar curvatureKähler–Einstein & K-stability https://neckpinch.com/papers/2610.40994/arxiv:2610.40994Thu, 29 Oct 2026 00:00:00 GMTErnani Ribeiro, Hung Tran — We classify complete, non-compact, simply connected, irreducible four-dimensional steady gradient Ricci solitons that are globally conformally Kähler and have an isoparametric potential. The steady Ricci solitons are U(2)-invariant nuts on ℝ⁴, including the Bryant and Cao solitons, and bolts on S² × ℝ² and on 𝓞(−m)→ℂP}¹. For each m≥3 there is exactly one non-collapsed bolt. A key step, valid for Ricci solitons of every sign, is that away from the locally conformally flat case, the conformal factor is aligned with the potential function, which yields cohomogeneity-one symmetry.Ricci solitonsKähler–Ricci solitons(Non)collapsing4-manifoldsKähler geometryHomogeneous spacesBoundaries & non-compact https://neckpinch.com/papers/2610.38137/arxiv:2610.38137Wed, 28 Oct 2026 00:00:00 GMTTomoyuki Hisamoto, Masataka Iwai — Inspired by recent work of Inoue and Hallam-Lahdili, we prove an equivariant Miyaoka-Yau inequality with a correction term for smooth Fano manifolds admitting Kähler-Ricci solitons. It recovers the usual Miyaoka-Yau inequality in the Kähler-Einstein case. Our proof uses weighted equivariant Bogomolov-Gieseker and Langer inequalities for torsion-free sheaves, together with a weighted slope estimate for the canonical extension sheaf. We also construct toric examples showing that the existence of a soliton implies neither weighted semistability of the canonical extension sheaf nor nonnegativity of the equivariant Miyaoka-Yau number.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryKähler–Einstein & K-stability https://neckpinch.com/papers/2610.34340/arxiv:2610.34340Sun, 25 Oct 2026 00:00:00 GMTJunhao Tian, Kai Zheng — In this paper, we prove the long time existence of the pseudo-Calabi flow on a compact toric variety for any Tⁿ-invariant initial Kähler metric. If the Mabuchi functional is proper modulo automorphisms, the flow converges exponentially to a constant scalar curvature Kähler (cscK) metric. In particular, this gives a flow proof that properness of the K-energy implies the existence of a cscK metric in the toric setting.Other curvature flowsKähler geometryScalar curvatureLong-time existence & convergenceKähler–Einstein & K-stability https://neckpinch.com/papers/2610.31270/arxiv:2610.31270Thu, 22 Oct 2026 00:00:00 GMTHongyu Chen, Li Ma, Li Sheng — We study the volume-normalized gradient flow of the squared Chern scalar curvature on compact Hermitian manifolds of complex dimension n≥3. The flow extends smoothly past a finite time if the spatial supremum of Chern scalar curvature belongs to L² in time. A uniform curvature bound in the evolving L^p norm, for one fixed p>n, gives global existence and smooth convergence of the whole trajectory to a constrained critical metric. On Chern scalar-flat backgrounds, small initial L^p curvature gives exponential convergence to the background. A corresponding condition on the trace-free first Chern–Ricci form gives exponential convergence on Chern–Ricci-flat Hermitian and positive Kähler–Einstein backgrounds. The smallness thresholds are independent of the initial higher derivatives. We also construct constant Chern scalar curvature backgrounds of either sign with arbitrarily small smooth perturbations whose solutions, if global, cannot converge back to the background.Other curvature flowsEinstein metricsRicci-flat & Calabi–YauSingularitiesKähler geometryScalar curvatureLong-time existence & convergenceKähler–Einstein & K-stability https://neckpinch.com/papers/2610.31068/arxiv:2610.31068Thu, 22 Oct 2026 00:00:00 GMTLi Ma, Li Sheng — In this paper, we propose the Chern-Calabi Flow for extremal metrics in conformal Hermitian geometry. After the existence of extremal metric, we consider the existence of global flows to the Chern-Calabi flows for extremal metrics on compact complex surfaces with Gauduchon metrics. To achieve this goal, we use the Adams inequality and the Gronwall inequality method to obtain fourth order derivative norm estimates. We also study the convergence of the global solution to the Chern-Calabi flow and its limit is the solution of the Chern-Calabi extremal metric problem. We propose a fourth order elliptic problem and derive the Bochner formula relevant to the elliptic estimates for the Chern-Calabi heat flow.Other curvature flowsKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability https://neckpinch.com/papers/2610.28238/arxiv:2610.28238Tue, 20 Oct 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove that every complete Kähler–Ricci shrinker with nonnegative Ricci curvature is holomorphically isometric to ℂ^k× N^(n-k) for some 0≤ k≤ n, where ℂ^k is the Gaussian shrinker and N is a compact Kähler–Ricci shrinker with nonnegative Ricci curvature. As a corollary, every complete Kähler–Ricci shrinker with quasi-positive Ricci curvature is compact.Ricci solitonsKähler geometry https://neckpinch.com/papers/2610.25745/arxiv:2610.25745Mon, 19 Oct 2026 00:00:00 GMTYuerong Bian, Xu Xu — We study the combinatorial Calabi flow associated with vertex scalings on infinitely triangulated surfaces with piecewise Euclidean and piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and an ε-uniformly nondegenerate initial metric, we establish short-time existence of smooth solutions and prove uniqueness among solutions that are continuous in the L^∞ norm.Other curvature flowsKähler geometryStability & uniquenessHarmonic maps & DeTurck trickDiscrete & graph Ricci https://neckpinch.com/papers/2610.24825/arxiv:2610.24825Sat, 17 Oct 2026 00:00:00 GMTRandall R. Van Why — We demonstrate that Kähler-Ricci flow on a Fano surface decomposes as a symplectic deflation along a plurianticanonical divisor plus an exact symplectic deformation in the divisor complement. We apply this decomposition to the study of certain projective bundles. We establish the optimal decay rate in the setting of Song, Székelyhidi, and Weinkove for a family of toric metrics which match the cohomological profile of Kähler-Ricci flow. In doing so, we identify a C²-obstruction to proving the optimal decay rate in the setting of ruled toric surfaces. We present these ideas as a new symplectic-topological approach to the study of Kähler-Ricci flow.Ricci flowKähler–Ricci flowKähler geometry https://neckpinch.com/papers/2610.22941/arxiv:2610.22941Fri, 16 Oct 2026 00:00:00 GMTWangjian Jian, Jian Song — In this paper, we establish geometric consequences of our Type I scalar curvature estimate for finite-time solutions of the Kähler-Ricci flow on compact Kähler manifolds. We prove a uniform global diameter bound and a Type I diameter bound for every fibre of finite time holomorphic contraction. These estimates yield Gromov-Hausdorff convergence to a unique compact metric space homeomorphic to the normal Kähler space determined by the limiting cohomology class. We also establish a local partial C⁰ estimate for the normalized flow and show that the tangent shrinkers are normal complex analytic varieties with log terminal singularities.Ricci flowKähler–Ricci flowRicci solitonsSingularitiesKähler geometryScalar curvatureLimit spaces & RCDAnalytic minimal model program https://neckpinch.com/papers/2610.21934/arxiv:2610.21934Thu, 15 Oct 2026 00:00:00 GMTFrederick Tsz-Ho Fong, Junbang Liu — Let X be a compact Kähler manifold with semi-ample canonical bundle. For any Kähler class [ω], Jian–Shi–Song proved that there exists a unique cscK metric in the class 2πc₁(K_X)+ε[ω] when ε∈ (0,ε₀], using the properness criterion of Chen–Cheng. We prove that the cscK metrics in 2πc₁(K_X)+ε[ω] converge, as εdownarrow0, in the Gromov–Hausdorff topology to the metric completion of the twisted Kähler-Einstein metric on the canonical model of X as conjectured by Jian–Shi–Song. Based on the technique developed in this paper, we can also give a new proof the theorem of Lee–Tosatti–Zhang on the Gromov-Hausdorff convergence of the normalized Kähler–Ricci flow on X.Ricci flowKähler–Ricci flowEinstein metricsKähler geometryScalar curvatureLimit spaces & RCDKähler–Einstein & K-stabilityAnalytic minimal model program https://neckpinch.com/papers/2610.21824/arxiv:2610.21824Thu, 15 Oct 2026 00:00:00 GMTLei Zhang, Zhenlei Zhang — In this paper, we study heat kernel estimates along the Kähler-Ricci flow with finite time noncollapsing singularities over a compact Kähler manifold. The starting point is the type-II scalar-curvature estimate, which gives the natural parabolic scale r≲ T-t near the singular time. By combining the distance distortion and space-time cut-off estimates of Bamler–Zhang with entropy, mean-value inequality, and conjugate heat-kernel estimates, we obtain two-sided Gaussian bounds and gradient bounds that are uniform on this scale. Under the global type-I scalar-curvature estimate, the same estimates hold on every scale. We then use these estimates and the monotonicity of the W₁-distance between conjugate heat flows to construct a canonical singular-time pseudo-distance. The distances dₜ (induced by ω(t)) converge uniformly to this pseudo-distance. Its metric quotient is the unique Gromov–Hausdorff limit. Finally, we apply Bamler's theory and the recent work of Hallgren–Zhang to obtain the following. Every fixed-base-point type-I blow-up admits a subsequential metric-flow limit whose time slices are singular shrinking Kähler–Ricci soliton spaces with normal complex-analytic and log-terminal structure, unique tangent cones, and a polarized Fano fibration. For moving base points, the limiting metric flow, equipped with its limiting conjugate heat flow, is a metric soliton precisely under an entropy-pinching condition.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsSingularities(Non)collapsingHeat kernelCurvature pinchingKähler geometryScalar curvature https://neckpinch.com/papers/2610.11935/arxiv:2610.11935Thu, 08 Oct 2026 00:00:00 GMTMatheus Horácio, Wenqi Li, Jianyu Ou, Guoqiang Wu, Detang Zhou — Let (M^(2m),g,f,J) be a complete nonsteady gradient Kähler-Ricci soliton satisfying Ric+∇² f=λg, λ≠ 0. We prove that constant scalar curvature forces the soliton to be rigid. More precisely, the universal cover splits holomorphically and isometrically as N^(2k)×ℂ^(m-k), where N^(2k) is Kähler-Einstein with Ric_(g_N)=λg_N. In the shrinking case the quotient is trivial; in the normalization λ=1/2 one has R≡ k. The Kähler result rests on a Riemannian rigidity criterion. On a complete nonsteady gradient Ricci soliton, if 𝓛_∇fRic is nonnegative or nonpositive everywhere, then it vanishes and the soliton is rigid; no assumption on the scalar curvature is needed. Along the Ricci flow generated by the soliton, this means that a Ricci tensor that is monotone in time is constant in time, and that this forces rigidity. We also give a direct proof that the pinching 0≤Ric≤λg forces constant scalar curvature and radial flatness, yielding the rigidity conclusion through the Petersen-Wylie characterization. The proof combines a weighted cutoff argument with a partial Codazzi symmetry for the Ricci endomorphism.Ricci flowRicci solitonsKähler–Ricci solitonsEinstein metricsCurvature pinchingKähler geometryScalar curvatureStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/2610.08233/arxiv:2610.08233Tue, 06 Oct 2026 00:00:00 GMTShaochuang Huang, Zhuo Peng — In this paper, we study strong uniqueness for smooth instantaneously complete Chern-Ricci flows on noncompact complex manifolds. Under suitable reference metric and positivity assumptions, we establish strong uniqueness for initial Hermitian metrics which are Kähler outside a compact set. The initial metric may be incomplete, and no curvature, metric comparison, or growth bounds are imposed on the evolving solutions. In particular, we obtain strong uniqueness from complete initial metrics in this class with bounded Chern-Ricci curvature. We also prove stationarity of flows from the Euclidean metric on ℂⁿ and uniqueness of the instantaneously complete flow from the Euclidean metric on the complex unit ball for all positive time. Finally, on complex surfaces, we show that a Ricci flow remaining Hermitian for a fixed complex structure is Kähler at all times if it is Kähler at one time, and derive a corresponding strong uniqueness result for Ricci flows in this class.Ricci flowGeneralized & G₂ flowsKähler geometryStability & uniquenessBoundaries & non-compact https://neckpinch.com/papers/2610.07897/arxiv:2610.07897Tue, 06 Oct 2026 00:00:00 GMTGiovanni Gentili, Luigi Vezzoni — We study the HKT geometry of compact locally conformally hyperkähler manifolds. We prove that on these manifolds the quaternionic Monge-Ampère equation is always solvable, extending results of Alesker and of Dinew-Sroka, and we confirm the conjecture on the maximal existence time of the HKT-Ricci flow. On quaternionic Hopf surfaces we construct non-trivial HKT solitons and prove convergence of the normalized flow for symmetric initial data.Ricci flowRicci-flat & Calabi–YauKähler geometryHomogeneous spaces https://neckpinch.com/papers/2610.05643/arxiv: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://neckpinch.com/papers/2610.05217/arxiv:2610.05217Sun, 04 Oct 2026 00:00:00 GMTHaozhao Li, Bing Wang, Kai Zheng — We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.Other curvature flowsSingularitiesKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability https://neckpinch.com/papers/2610.05201/arxiv:2610.05201Sun, 04 Oct 2026 00:00:00 GMTLiding Huang, Xiaohua Zhu — We first define an extended Mabuchi functional for a class of generalized Kähler metrics of symplectic type on a toric Fano manifold (M,J,T), and prove it is proper. Then by showing the monotonicity of functional along the normalized generalized Kähler-Ricci flow for any initial T-invariant generalized Kähler metric with its symplectic form in 2πc₁(M,J), we prove that the flow converges to a Kähler-Ricci soliton. The result confirms a conjecture of Apostolov-Streets-Ustinovskiy.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsKähler geometryKähler–Einstein & K-stability https://neckpinch.com/papers/2610.03592/arxiv: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://neckpinch.com/papers/2610.02164/arxiv: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://neckpinch.com/papers/2610.01643/arxiv:2610.01643Thu, 01 Oct 2026 00:00:00 GMTYeyun Xu, Linfeng Zhou — We establish a Type I curvature bound for finite-time volume-collapsing Kähler–Ricci flows on compact Kähler surfaces. No symmetry assumption is imposed, and the initial Kähler class need not be rational. The proof combines local symplectic topology with the classification of gradient Kähler–Ricci shrinking solitons. Bamler's compactness and structure theory provides the shrinking limits used in the argument.Ricci flowKähler–Ricci flowRicci solitonsSingularities(Non)collapsingKähler geometryLimit spaces & RCD https://neckpinch.com/papers/2610.01202/arxiv:2610.01202Thu, 01 Oct 2026 00:00:00 GMTJiyuan Han — We prove a uniform L^∞-estimate for the parabolic Monge–Ampère equation under uniform Hörmander-Tian type estimates with respect to the initial and prescribed measures. We apply this estimate to rescaled Kähler–Ricci flows on a family of polarized Calabi–Yau manifolds over the punctured disk. An interpolation argument gives uniform Hörmander-Tian type estimates along the flows. We also establish uniform diameter bounds and Gromov–Hausdorff precompactness for this family of flows. In particular, we obtain an alternative proof of the diameter estimate by Li-Tosatti.Ricci flowKähler–Ricci flowRicci-flat & Calabi–YauKähler geometryLimit spaces & RCD https://neckpinch.com/papers/2609.39620/arxiv:2609.39620Wed, 30 Sep 2026 00:00:00 GMTWangjian Jian, Jian Song — We establish the Type I estimate for the scalar curvature of the Kahler-Ricci flow on compact Kahler manifolds, for arbitrary smooth initial metrics, whenever the flow develops finite time singularities. This estimate is a building block for the analytic minimal model program with Ricci flow.Ricci flowKähler–Ricci flowSingularitiesKähler geometryScalar curvatureAnalytic minimal model program https://neckpinch.com/papers/2609.36418/arxiv:2609.36418Tue, 29 Sep 2026 00:00:00 GMTWenqi Li, Jianyu Ou, Guoqiang Wu, Detang Zhou — Let (M^(2m),g,f,J) be a complete gradient Kähler–Ricci shrinker satisfying Ric+∇² f=1/2 g. We prove that if the scalar curvature is constant, then the soliton is rigid. More precisely, there exists an integer k∈\0,…,m\ such that R≡ k and (M^(2m),g,J)≅ bigl(N^(2k)×ℂ^(m-k), g_N+g_Euc,J_N⊕ J₀bigr), where (N^(2k),g_N,J_N) is Kähler–Einstein and Ric_(g_N)=1/2 g_N. As part of the proof, we establish a Riemannian rigidity criterion: for a complete nonsteady gradient Ricci soliton with constant scalar curvature, the condition 𝓛_∇fRic=0 implies radial flatness and hence rigidity.Ricci solitonsEinstein metricsKähler geometryScalar curvatureStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/2609.29359/arxiv:2609.29359Thu, 24 Sep 2026 00:00:00 GMTMatheus Andrade Ribeiro de Moura Horácio — We prove that every complete nonsteady gradient Kähler-Ricci soliton with constant scalar curvature is rigid. This establishes Cao's rigidity conjecture for Kähler-Ricci solitons in arbitrary dimension and gives the corresponding result for expanding solitons, without additional curvature assumptions. The proof uses a rigidity criterion for gradient Ricci solitons with constant scalar curvature, expressed by the vanishing of the Lie derivative of the Ricci tensor along the soliton vector field. In the Kähler case, this vanishing follows from constant scalar curvature, the closedness of the Ricci form, and the classical real holomorphicity of the soliton vector field.Ricci solitonsKähler–Ricci solitonsKähler geometryScalar curvatureStability & uniqueness https://neckpinch.com/papers/2609.28280/arxiv:2609.28280Wed, 23 Sep 2026 00:00:00 GMTLorenzo Foscolo, Mario Garcia-Fernandez — The IIB system is a system of PDEs for an SU(3)–structure and a positive function on a 6-manifold. Its solutions describe conformally balanced pluriclosed Hemitian metrics on complex 3-folds with holomorphically trivial canonical line bundle. In particular, solutions of the IIB system are steady solitons for the generalized Ricci-flow and Bismut–Hermitian–Einstein metrics. In this paper we study cohomogeneity one solutions of the IIB system. We construct 1-parameter families (up to scaling symmetries) of complete non-compact non-Kähler solutions on the smoothing of the conifold with controlled geometry at infinity. The generic member of the family is asymptotically conical with tangent cone at infinity the Calabi–Yau cone metric on the conifold. As a limit of the family we recover an explicit solutions known in the physics literature as the Chamseddine–Volkov/Maldacena–Nuñez solution, which has an exotic asymptotic geometry. We show that there are no complete cohomogeneity one solutions on crepant resolutions of the conifold (or its quotient), but we also establish the existence of an analogous 1-parameter family of forward complete solutions defined on exterior domains of the conifold with prescribed incomplete behaviour along the interior boundary and similar asymptotic behaviour at infinity. As a byproduct of these existence results, we produce infinitely many complete non-compact non-Kähler Bismut–Hermitian–Einstein metrics in complex dimension 3 with full holonomy of the Bismut connection, in contrast to the holonomy reduction forced upon compact examples. We also find infinitely many such complete non-compact full-holonomy non-Kähler examples (with at least two ends) in complex dimension 2 by revisiting a construction due to Callan–Harvey–Strominger in the physics literature.Ricci flowGeneralized & G₂ flowsRicci solitonsEinstein metricsRicci-flat & Calabi–Yau3-manifoldsKähler geometryHomogeneous spacesBoundaries & non-compact https://neckpinch.com/papers/2609.24884/arxiv:2609.24884Mon, 21 Sep 2026 00:00:00 GMTTristan C. Collins, Genggeng Huang, Freid Tong, Yulun Xu — We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.Ricci solitonsKähler–Ricci solitonsKähler geometryAnalytic minimal model program https://neckpinch.com/papers/2609.23630/arxiv:2609.23630Sun, 20 Sep 2026 00:00:00 GMTYasufumi Nitta — We prove that every extremal Kähler–Ricci soliton on a Fano manifold is Kähler–Einstein. This solves the problem of Calamai and Petrecca in full generality.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryKähler–Einstein & K-stability