Space of Kähler metrics (IV)--On the lower bound of the K-energy

2008/09/24 by Xiuxiong Chen, Chen, Xiuxiong · 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.0809.4081

openalex publication_date 2008/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We partially confirm an old conjecture of Donaldson that if there exists a cscK metrics in a given Kähler class, then there is no degenerated geodesic ray which is tamed by a bounded ambient geometry unless it parallels to a holomorphic line consists of cscK metrics only. We also prove that for simple test configuration where the central fibre has a cscK metric, the K energy functionals in the nearby fibre must also have a uniform lower bound in its underlying Kähler class.

Citations

• Interior estimates for solutions of Abreu's equation
• Test configurations and Geodesic rays

Cited by

• Convergence of Kähler-Ricci flow on Fano manifolds, II
• Extremal Kähler metrics and energy functionals on projective bundles

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