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

Qiʼan Guan; Xiangyu Zhou; Langfeng Zhu

doi:10.1016/j.crma.2011.06.001

Analytic Geometry

On the Ohsawa–Takegoshi

L^{2}

extension theorem and the twisted Bochner–Kodaira identity

Presented by: Jean-Pierre Demailly

Qiʼan Guan ¹; Xiangyu Zhou ²; Langfeng Zhu 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, Volume 349 (2011) no. 13-14, pp. 797-800.

Abstract
Résumé

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.

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.

Received: 2011-01-13
Accepted: 2011-06-01
Published online: 2011-06-22

DOI: 10.1016/j.crma.2011.06.001

Author's affiliations:

Qiʼan Guan ¹; Xiangyu Zhou ²; Langfeng Zhu 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

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     author = {Qi'an Guan and Xiangyu Zhou and Langfeng Zhu},
     title = {On the {Ohsawa{\textendash}Takegoshi} $ {L}^{2}$ extension theorem and the twisted {Bochner{\textendash}Kodaira} identity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {797--800},
     publisher = {Elsevier},
     volume = {349},
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     year = {2011},
     doi = {10.1016/j.crma.2011.06.001},
     language = {en},
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Qiʼan Guan; Xiangyu Zhou; Langfeng Zhu. On the Ohsawa–Takegoshi $ {L}^{2}$ extension theorem and the twisted Bochner–Kodaira identity. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 797-800. doi : 10.1016/j.crma.2011.06.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.001/

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