An asymptotic slope of the α-K-energy for the Kahler-Yang-Mills equations

2025/12/15 by Akito Futaki, Futaki, Akito, Jianwei Shi +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2512.12897

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

For holomorphic vector bundles over compact Kähler manifolds, we establish a formula for the asymptotic slope of the α-K-energy associated with the Kahler-Yang-Mills equations.

Citations

• Geodesic Rays in the Donaldson--Uhlenbeck--Yau Theorem
• Stability conditions for polarised varieties
• Uniform K-stability and asymptotics of energy functionals in Kähler geometry
• Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
• Test Configurations for K-Stability and Geodesic Rays

Related

• J-equation on holomorphic vector bundles
• Coupled equations for Kähler metrics and Yang-Mills connections (Thesis)
• The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds
• On the Kähler-Yang-Mills-Higgs equations
• On Yang-Mills connections on compact Kähler surfaces