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