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

Xiangyu Zhou and Langfeng Zhu

Vol. 309 (2020), No. 2, 475–510

DOI: 10.2140/pjm.2020.309.475

Abstract

We obtain optimal $L^2$ 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