Comptes Rendus
Analyse et géométrie complexes
Optimal L 2 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 L 2 pour les formes ouvertes sur les variété Kähler faiblement pseudoconvexes. Nous prouvons les propriétés de produit de certaines extensions minimales de L 2 , qui généralisent les propriétés de produit du noyau Bergman. Sur la base de la concavité logarithmique de certaines intégrales minimales de L 2 , nous donnons une méthode différente pour la conjecture de Suita et son extension.

We establish several optimal L 2 extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal L 2 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 L 2 integrals.

Reçu le :
Accepté le :
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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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