$L^2$ extension theorem for jets with variable denominators

Sheng Rao; Runze Zhang

doi:10.5802/crmath.167

Complex analysis

L^{2}

extension theorem for jets with variable denominators

Sheng Rao ^1,²; Runze Zhang ³

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China
² Université de Grenoble-Alpes, Institut Fourier (Mathématiques) UMR 5582 du C.N.R.S., 100 rue des Maths, 38610 Gières, France
³ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China.

Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 181-193.

Abstract

By studying the variable denominators introduced by X. Zhou–L. Zhu, we generalize the results of D. Popovici for the $L^{2}$ extension theorem for jets. As a direct corollary, we also give a generalization of T. Ohsawa–K. Takegoshi’s extension theorem to a jet version.

Received: 2020-10-16
Accepted: 2020-12-13
Published online: 2021-03-17

DOI: 10.5802/crmath.167

Classification: 32D15, 32L10, 32Q15, 32T35
Keywords: Continuation of analytic objects in several complex variables; Sheaves and cohomology of sections of holomorphic vector bundles, general results, Kähler manifolds, Exhaustion functions

Author's affiliations:

Sheng Rao ^{1, 2}; Runze Zhang ³

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China
² Université de Grenoble-Alpes, Institut Fourier (Mathématiques) UMR 5582 du C.N.R.S., 100 rue des Maths, 38610 Gières, France
³ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Sheng Rao and Runze Zhang},
     title = {$L^2$ extension theorem for jets with variable denominators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {181--193},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {2},
     year = {2021},
     doi = {10.5802/crmath.167},
     language = {en},
}

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Sheng Rao; Runze Zhang. $L^2$ extension theorem for jets with variable denominators. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 181-193. doi : 10.5802/crmath.167. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.167/

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