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.
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Keywords: Mabuchi’s functional, variational method, cscK metrics
Mot clés : fonction de Mabuchi, méthode variationelle, métriques cscK
@article{AIF_2018__68_2_805_0, author = {Li, Long}, title = {Subharmonicity of conic {Mabuchi{\textquoteright}s} functional, {I}}, journal = {Annales de l'Institut Fourier}, pages = {805--845}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {2}, year = {2018}, doi = {10.5802/aif.3178}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.3178/} }
TY - JOUR AU - Li, Long TI - Subharmonicity of conic Mabuchi’s functional, I JO - Annales de l'Institut Fourier PY - 2018 SP - 805 EP - 845 VL - 68 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3178/ DO - 10.5802/aif.3178 LA - en ID - AIF_2018__68_2_805_0 ER -
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. http://www.numdam.org/articles/10.5802/aif.3178/
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