Vol. 309, No. 2, 2020

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Optimal $L^2$ extension of sections from subvarieties in weakly pseudoconvex manifolds

Xiangyu Zhou and Langfeng Zhu

Vol. 309 (2020), No. 2, 475–510
Abstract

We obtain optimal L2 extension of holomorphic sections of a holomorphic vector bundle from subvarieties in weakly pseudoconvex Kähler manifolds. Moreover, in the case of a line bundle the Hermitian metric is allowed to be singular.

Keywords
optimal $L^2$ extension, plurisubharmonic function, multiplier ideal sheaf, strong openness, weakly pseudoconvex manifold, Kähler manifold
Mathematical Subject Classification 2010
Primary: 32D15, 32J25, 32Q15, 32U05, 32W05
Secondary: 14F18, 32L10
Milestones
Received: 27 September 2019
Revised: 5 June 2020
Accepted: 17 November 2020
Published: 14 January 2021
Authors
Xiangyu Zhou
Institute of Mathematics, AMSS
and
Hua Loo-Keng Key Laboratory of Mathematics
Chinese Academy of Sciences
Beijing
China
Langfeng Zhu
School of Mathematics and Statistics
Wuhan University
Wuhan
China