Geometric regularity of blow-up limits of the Kähler-Ricci flow

2023/10/11 by Max Hallgren, Wangjian Jian, Hallgren, Max +5 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2310.08610

openalex publication_date 2023/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-W₁ distance. In particular, the singular sets of each time slice and its tangent cones are close and of codimension no less than 4.

Cited by

• Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
• Fano Fibrations and Twisted Kähler-Einstein Metrics I

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