Optimal constant problem in the $ {L}^{2}$ extension theorem

Qiʼan Guan; Xiangyu Zhou

doi:10.1016/j.crma.2012.08.007

Complex Analysis

Optimal constant problem in the

L^{2}

extension theorem
[Problème de la constante optimale dans le théorème dʼextension

L^{2}

]

Présenté par : Jean-Pierre Demailly

Qiʼan Guan ¹ ; Xiangyu Zhou ²

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

Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 753-756.

Résumé
Abstract

Dans cette Note, nous résolvons le problème de la détermination de la constante optimale dans le théorème dʼextension $L^{2}$ avec poids négligeable sur les variétés de Stein. En application, nous prouvons la conjecture de Suita sur des surfaces de Riemann arbitraires.

In this Note, we solve the optimal constant problem in the $L^{2}$ -extension theorem with negligible weight on Stein manifolds. As an application, we prove the Suita conjecture on arbitrary open Riemann surfaces.

Reçu le : 2012-07-04
Accepté le : 2012-08-29
Publié le : 2012-08-01

DOI : 10.1016/j.crma.2012.08.007

Affiliations des auteurs :

Qiʼan Guan ¹ ; Xiangyu Zhou ²

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

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Qiʼan Guan; Xiangyu Zhou. Optimal constant problem in the $ {L}^{2}$ extension theorem. Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 753-756. doi : 10.1016/j.crma.2012.08.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.08.007/

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YUTA WATANABE DUAL NAKANO POSITIVITY AND SINGULAR NAKANO POSITIVITY OF DIRECT IMAGE SHEAVES, Nagoya Mathematical Journal (2024), p. 1 | DOI:10.1017/nmj.2024.20
Qi’an Guan; Zhitong Mi; Zheng Yuan Optimal $L^{2}$ Extension for Holomorphic Vector Bundles with Singular Hermitian Metrics, Peking Mathematical Journal (2024) | DOI:10.1007/s42543-024-00085-9
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