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arXiv · 2610.22941

Type I estimates for the Kähler-Ricci flow II

Wangjian Jian·Jian Song
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Abstract

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 $C^0$ estimate for the normalized flow and show that the tangent shrinkers are normal complex analytic varieties with log terminal singularities.

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Wangjian Jian, Jian Song. 2026-10-16. Type I estimates for the Kähler-Ricci flow II. https://arxiv.org/abs/2610.22941

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