An $ {L}^{2}$ extension theorem with optimal estimate

Qiʼan Guan; Xiangyu Zhou

doi:10.1016/j.crma.2013.12.007

Analytic geometry

L^{2}

extension theorem with optimal estimate
[Un théorème dʼextension

L^{2}

avec estimation optimale]

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 352 (2014) no. 2, pp. 137-141.

Résumé
Abstract

Dans cette note, nous présentons un théorème dʼextension $L^{2}$ avec estimation optimale, pour des fibrés vectoriels holomorphes semi-positifs dans le sens de Nakano. Ce résultat implique aussi des versions optimales pour lʼestimation de divers autres théorèmes dʼextension $L^{2}$ . En application, nous obtenons la solution du cas dʼégalité dans une conjecture de Suita relative aux capacité logarithmiques de surfaces de Riemann ouvertes, ainsi que la solution de la conjecture de Suita généralisée, et la confirmation dʼun énoncé connu sous le nom de L-conjecture.

In this note, we establish an $L^{2}$ extension theorem with an optimal estimate for semi-positive vector bundles in the sense of Nakano. This result also implies optimal estimate versions of various $L^{2}$ extension theorems. Applications include a solution of the equality case in a conjecture of Suita on logarithmic capacities of open Riemann surface, as well as a solution of the extended Suita conjecture and a confirmation of the so-called L-conjecture.

Reçu le : 2013-08-11
Accepté le : 2013-12-05
Publié le : 2014-01-08

DOI : 10.1016/j.crma.2013.12.007

Affiliations des auteurs :

Qiʼan Guan ¹ ; Xiangyu Zhou ²

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Qiʼan Guan; Xiangyu Zhou. An $ {L}^{2}$ extension theorem with optimal estimate. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 137-141. doi : 10.1016/j.crma.2013.12.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.007/

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