Subharmonicity of conic Mabuchi’s functional, I
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 805-845.

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.

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.

Published online:
DOI: 10.5802/aif.3178
Classification: 32U05, 53C55, 35J35
Keywords: Mabuchi’s functional, variational method, cscK metrics
Li, Long 1

1 Department of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, ON L8S 4K1 (Canada)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Li, Long. Subharmonicity of conic Mabuchi’s functional, I. Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 805-845. doi : 10.5802/aif.3178.

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