Subharmonicity of conic Mabuchi's functional, I

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.

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

References in corpus (4)

• The Space of Kähler metrics (II)
• Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors
• Geodesics in the space of Kähler cone metrics
• Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature

Cited by in corpus (3)

• Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor
• Construction of constant scalar curvature Kähler cone metrics
• Regularization of plurisubharmonic functions with a net of good points