Uniform estimates for cscK metrics

Deruelle, Alix; Di Nezza, Eleonora

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 3, pp. 975-993.

Cette note est le fruit d’une série d’exposés donnés à Cortona en 2019 et dont le but visait à comprendre les avancées majeures due à Chen et Cheng sur l’existence de métriques kähleriennes à courbure scalaire constante. Nous donnons ici une preuve alternative et détaillée des estimées a priori dites $C^0$ et $C^2$ dans le cadre de la théorie du pluripotentiel.

This note grew out of a series of lectures held in Cortona in 2019 and whose aim was to understand the recent breakthrough obtained by Chen and Cheng on the existence of constant scalar curvature Kähler metrics. We present a detailed version of the $C^0$ and $C^2$ a priori estimates within the realm of pluripotential theory.

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