https://neckpinch.com/authors/zhenlei-zhang/New arXiv papers by Zhenlei Zhang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.28238arxiv: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://arxiv.org/abs/2610.21824arxiv: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://arxiv.org/abs/2609.18834arxiv:2609.18834Wed, 16 Sep 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove that any finite-time collapsing Kähler-Ricci flow on compact Kähler surfaces develops a Type I singularity. Together with the previous results, this implies that any finite time singularity of the Kähler-Ricci flow on compact Kähler surfaces is of Type I.Ricci flowKähler–Ricci flowSingularities(Non)collapsingKähler geometry https://arxiv.org/abs/2609.01442arxiv:2609.01442Tue, 01 Sep 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove that any finite time collapsing Kähler Ricci flow on ruled surfaces develops a Type I singularity, such singularity is modeled on the standard product shrinker ℙ¹× ℂ. As an application, we obtain the optimal collapse rate of fibers on ruled surfaces.Ricci flowKähler–Ricci flowRicci solitonsSingularities(Non)collapsingKähler geometry https://arxiv.org/abs/2608.17458arxiv:2608.17458Tue, 18 Aug 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove the Feldman–Ilmanen–Knopf conjecture for finite time Type I singularities of the Kähler–Ricci flow. More precisely, for any compact Kähler manifold Y and its blow-up π:BlₚY⟶ Y, if [ω₀]−Tc₁(M)=π^*[ω_Y], then any Type I parabolic blow-up limit of the Kähler Ricci flow along the exceptional divisor is the FIK shrinker Tot(𝓞_(ℙⁿ⁻¹)(−1)).Ricci flowKähler–Ricci flowRicci solitonsSingularitiesKähler geometryAnalytic minimal model program https://arxiv.org/abs/2608.10953arxiv:2608.10953Tue, 11 Aug 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — In this paper, we study compactness, rigidity, and related geometric properties of complete Kähler Ricci shrinkers through the polarized Fano fibration structure.Ricci solitonsKähler geometryLimit spaces & RCDStability & uniquenessAnalytic minimal model program https://arxiv.org/abs/2606.17402arxiv:2606.17402Tue, 16 Jun 2026 00:00:00 GMTLei Zhang, Zhenlei Zhang — This paper is concerned with a class of the long time Kähler-Ricci flow on a compact Kähler manifold. It is shown that the uniform μ-entropy or uniform Sobolev inequality along the normalized Kähler-Ricci flow with semiample canonical bundle. As a consequence, we prove that the scalar curvature of the Kähler metrics along the normalized Kähler-Ricci flow converge to negative Kodaira dimension of the compact Kähler manifold.Ricci flowKähler–Ricci flowKähler geometryScalar curvatureAnalytic minimal model program https://arxiv.org/abs/2509.14820arxiv:2509.14820Thu, 18 Sep 2025 00:00:00 GMTGang Tian, Qi S. Zhang, Zhenlei Zhang, Meng Zhu, Xiaohua Zhu — We first prove a uniform integral Laplace comparison result for the Kähler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, using Cheeger-Colding theory and previous results by some of the authors, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of Kähler-Ricci flows, modulo a codimension 4 singular set. We also expounded on some existing literature on this conjecture.Ricci flowKähler–Ricci flow4-manifoldsKähler geometry