Work

Type I estimates for the Kähler-Ricci flow II

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.22941

Authors: Jian, Wangjian, Song, Jian

Institutions: Rutgers, The State University of New Jersey, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: G1603846912, Analysis and PDEs in complex geometry, G2781161061, G4708255020, G8167641167, G8533620077

OpenAlex ID: W7222954380

Cites: 27

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Related to: 10