On the Ohsawa–Takegoshi $ {L}^{2}$ extension theorem and the twisted Bochner–Kodaira identity

Guan, Qiʼan; Zhou, Xiangyu; Zhu, Langfeng

doi:10.1016/j.crma.2011.06.001

Analytic Geometry

On the Ohsawa–Takegoshi

L^{2}

extension theorem and the twisted Bochner–Kodaira identity
[Sur le théorème dʼextension

L^{2}

de Ohsawa–Takegoshi et lʼidentité tordue de Bochner–Kodaira]

Présenté par : Jean-Pierre Demailly

Guan, Qiʼan ¹ ; Zhou, Xiangyu ² ; Zhu, Langfeng ¹

¹ Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
² Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China

Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 797-800.

Résumé
Abstract

Dans cette Note, nous améliorons lʼestimation des constantes dans la généralisation par Ohsawa du théorème dʼextension $L^{2}$ de Ohsawa–Takegoshi concernant les fonctions holomorphes, et nous appliquons ce résultat à lʼétude de la conjecture de Suita. Nous présentons également une remarque permettant de généraliser le théorème dʼextension de Ohsawa–Takegoshi au cas des $(n - 1, q)$ -formes lisses $\bar{\partial}$ -fermées. Enfin, nous montrons que le facteur tordu dans lʼidentité tordue de Bochner–Kodaira peut être une fonction plurisuperharmonique non lisse.

In this Note, we improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi $L^{2}$ extension theorem for holomorphic functions by finding a smaller constant, and apply the result to the Suita conjecture. We also present a remark allowing to generalize the Ohsawa–Takegoshi extension theorem to the case of $\bar{\partial}$ -closed smooth $(n - 1, q)$ -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.

Reçu le : 2011-01-13
Accepté le : 2011-06-01
Publié le : 2011-06-22

DOI : 10.1016/j.crma.2011.06.001

Affiliations des auteurs :

Guan, Qiʼan ¹ ; Zhou, Xiangyu ² ; Zhu, Langfeng ¹

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     title = {On the {Ohsawa{\textendash}Takegoshi} $ {L}^{2}$ extension theorem and the twisted {Bochner{\textendash}Kodaira} identity},
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Guan, Qiʼan; Zhou, Xiangyu; Zhu, Langfeng. On the Ohsawa–Takegoshi $ {L}^{2}$ extension theorem and the twisted Bochner–Kodaira identity. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 797-800. doi : 10.1016/j.crma.2011.06.001. http://www.numdam.org/articles/10.1016/j.crma.2011.06.001/

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