Optimal $L^2$ Extensions of Openness Type and Related Topics

Wang Xu; Xiangyu Zhou

doi:10.5802/crmath.437

Analyse et géométrie complexes

Optimal

L^{2}

Extensions of Openness Type and Related Topics

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

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 679-683.

Résumé
Abstract

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 : 2022-02-05
Accepté le : 2022-10-16
Publié le : 2023-03-02

DOI : 10.5802/crmath.437

Classification : 32D15, 32A36, 32L05, 32W05, 32E10, 14C30, 30C40

Affiliations des auteurs :

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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     author = {Wang Xu and Xiangyu Zhou},
     title = {Optimal $L^2$ {Extensions} of {Openness} {Type} and {Related} {Topics}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {679--683},
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     year = {2023},
     doi = {10.5802/crmath.437},
     language = {en},
}

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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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