Uniform estimates for cscK metrics

Alix Deruelle; Eleonora Di Nezza

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

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

Résumé
Abstract

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.

Publié le : 2022-07-01

DOI : 10.5802/afst.1710

Affiliations des auteurs :

Alix Deruelle ¹ ; Eleonora Di Nezza ^{2, 3}

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Uniform estimates for {cscK} metrics},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {975--993},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 31},
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     doi = {10.5802/afst.1710},
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Alix Deruelle; Eleonora Di Nezza. Uniform estimates for cscK metrics. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 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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