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

Guan, Qiʼan; Zhou, Xiangyu

doi:10.1016/j.crma.2013.01.012

Analytic Geometry

Generalized

L^{2}

extension theorem and a conjecture of Ohsawa

Presented by: Jean-Pierre Demailly

Guan, Qiʼan ¹; Zhou, Xiangyu 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.

Abstract
Résumé

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.

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.

Received: 2012-11-30
Accepted: 2013-01-30
Published online: 2013-02-01

DOI: 10.1016/j.crma.2013.01.012

Author's affiliations:

Guan, Qiʼan ¹; Zhou, Xiangyu ²

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Guan, Qiʼan; Zhou, Xiangyu. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.01.012/

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Cited by Sources:

^☆ The second author was partially supported by NSFC.