Subharmonicity of conic Mabuchi's functional, I

2015/10/31 by Long Li, Li, Long · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1511.00178

Some errors and typos are corrected, and one Appendix is added to explain a new regularization technique for weak conic geodesics

openalex publication_date 2015/10/31 · arxiv created 2016/03/01 · arxiv updated 2016/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic cscK metrics are its critical points. Finally we proved the convexity of the conic Mabuchi functional along any conic geodesics.

Citations

• Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature

Cited by

• Existence of Conical Higher cscK Metrics on a Minimal Ruled Surface

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