Generalized $ {L}^{2}$ extension theorem and a conjecture of Ohsawa

Qiʼan Guan; Xiangyu Zhou

doi:10.1016/j.crma.2013.01.012

Analytic Geometry

Generalized

L^{2}

extension theorem and a conjecture of Ohsawa

Présenté par : Jean-Pierre Demailly

Qiʼan Guan ¹ ; Xiangyu Zhou ²

¹ Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China
² Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, China

Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 111-114.

Résumé
Abstract

Dans cet article, nous déterminons la constante optimale intervenant dans lʼestimée du théorème dʼextension $L^{2}$ généralisé de Ohsawa. Le résultat vaut pour les fibrés vectoriels holomorphes sur une classe de variétés complexes incluant à la fois les variétés de Stein et les variétés algébriques projectives complexes. Comme application, nous obtenons la solution dʼune conjecture correspondante dʼOhsawa.

In this paper, we determine the optimal constant in the estimate of Ohsawaʼs generalized $L^{2}$ extension theorem. The result holds for holomorphic vector bundles on a class of complex manifolds including both Stein manifolds and complex projective algebraic manifolds. As an application, we obtain a solution to a related conjecture of Ohsawa.

Reçu le : 2012-11-30
Accepté le : 2013-01-30
Publié le : 2013-02-01

DOI : 10.1016/j.crma.2013.01.012

Affiliations des auteurs :

Qiʼan Guan ¹ ; Xiangyu Zhou ²

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Qiʼan Guan; Xiangyu Zhou. Generalized $ {L}^{2}$ extension theorem and a conjecture of Ohsawa. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 111-114. doi : 10.1016/j.crma.2013.01.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.012/

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Cité par Sources :

^☆ The second author was partially supported by NSFC.

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