Subharmonicity of conic Mabuchi’s functional, I

Li, Long

Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 805-845.

Le but de cet article est de démontrer la convexité de la fonctionnelle de Mabuchi le long d’une géodésique dans le cadre conique. Nous considérons d’abord les métriques de Kähler de courbure scalaire constante (cscK) et ensuite nous introduisons la fonctionnelle de Mabuchi de sorte que les métriques coniques cscK soient ses points critiques. Par la suite nous démontrons le résultat principal.

The purpose of this paper is to prove the convexity of Mabuchi’s functional along a geodesic in the conic setting. We first establish a scheme to study conic constant scalar curvature Kähler (cscK) metrics, and then the conic Mabuchi functional is introduced in such a way that conic cscK metrics are its critical points. Finally we prove that the conic Mabuchi functional is convex and continuous along a conic geodesic.

Classification : 32U05, 53C55, 35J35
Keywords: Mabuchi’s functional, variational method, cscK metrics
Mot clés : fonction de Mabuchi, méthode variationelle, métriques cscK

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