2024/10/29 by Takahiro Aoi, Aoi, Takahiro
Mathematics · Medicine · Physics and Astronomy · #53C25 #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Medical Imaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2410.22090
openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we directly prove that if the limit of microscopic stability thresholds introduced by Berman for a polarized manifold satisfies some condition, then there exists a unique constant scalar curvature Kähler metric. This is an analogue of K.Zhang's result which is proved by the delta-invariant introduced by Fujita-Odaka. This work is motivated by Berman's result which shows that if a Fano manifold is uniformly Gibbs stable, then there exists a unique Kähler-Einstein metric, without uniform K-stability. We also give some sufficient conditions of the existence of a constant scalar curvature Kähler cone metric.