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Uniform estimates for cscK metrics
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 975-993.

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.

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.

Published online:
DOI: 10.5802/afst.1710
Alix Deruelle 1; Eleonora Di Nezza 2, 3

1 Institut de Mathématiques de Jussieu, Paris Rive Gauche (IMJ-PRG) UPMC - Campus Jussieu, 4, place Jussieu Boite Courrier 247 - 75252 Paris Cedex 05, France
2 Centre de Mathématiques Laurent Schwartz, École Polytechnique, Palaiseau Cedex, France
3 Institut de Mathématiques de Jussieu, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Alix Deruelle; Eleonora Di Nezza. Uniform estimates for cscK metrics. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 975-993. doi : 10.5802/afst.1710. https://afst.centre-mersenne.org/articles/10.5802/afst.1710/

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