https://neckpinch.com/authors/lei-zhang/New arXiv papers by Lei Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT 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/2606.17402/arxiv: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