The Partial C⁰-estimate along a general continuity path and applications

2019/09/08 by Ke Feng, Feng, Ke, Liangming Shen +1
Mathematics · #53C44 #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.1909.05196

openalex publication_date 2019/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a new partial C⁰-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted (1,1)-form on Fano manifolds. As an application, this estimate enables us to show the reductivity of the automorphism group of the limit space, which leads to a proof of Yau-Tian-Donaldson Conjecture admitting some types of holomorphic vector fields.

Citations

• Space of Ricci flows (II)
• On the Yau-Tian-Donaldson conjecture for singular Fano varieties
• On the existence of conic Kahler-Einstein metrics

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