Comptes Rendus
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Analyse et géométrie complexes
Optimal L2 Extensions of Openness Type and Related Topics
Wang Xu1  ; Xiangyu Zhou2
1 School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China
2 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 679-683.

Nous établissons quelques théorèmes d’extension optimaux L2 pour les formes ouvertes sur les variété Kähler faiblement pseudoconvexes. Nous prouvons les propriétés de produit de certaines extensions minimales de L2, qui généralisent les propriétés de produit du noyau Bergman. Sur la base de la concavité logarithmique de certaines intégrales minimales de L2, nous donnons une méthode différente pour la conjecture de Suita et son extension.

We establish several optimal L2 extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal L2 extensions, which generalizes the product property of Bergman kernels. We describe a different approach to the Suita conjecture and its generalizations, which is based on a log-concavity for certain minimal L2 integrals.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.437
Classification : 32D15, 32A36, 32L05, 32W05, 32E10, 14C30, 30C40

Wang Xu 1 ; Xiangyu Zhou 2

1 School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China
2 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Wang Xu; Xiangyu Zhou. Optimal $L^2$ Extensions of Openness Type and Related Topics. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 679-683. doi : 10.5802/crmath.437. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.437/

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