On the Ohsawa–Takegoshi L2 extension theorem and removable singularities of plurisubharmonic functions

Wang, Xieping

doi:10.2140/apde.2026.19.1395

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On the Ohsawa–Takegoshi $L^2$ extension theorem and removable singularities of plurisubharmonic functions

Xieping Wang

Vol. 19 (2026), No. 7, 1395–1416

DOI: 10.2140/apde.2026.19.1395

Abstract

The celebrated Ohsawa–Takegoshi extension theorem for $L^{2}$ holomorphic functions on bounded pseudoconvex domains in $ℂ^{n}$ is a fundamental result in the fields of complex analysis and algebraic geometry. In 1995, Ohsawa conjectured that the theorem holds more generally on bounded complete Kähler domains in $ℂ^{n}$ . Recently, Chen, Wu and Wang confirmed this conjecture in a special case. We extend their result to the case of holomorphic sections of twisted canonical bundles over relatively compact complete Kähler domains in Stein manifolds. As an application, we establish a Hartogs-type extension theorem for plurisubharmonic functions across compact complete pluripolar sets. This result complements a classical theorem of Shiffman and may be regarded as a plurisubharmonic analogue of the Skoda–El Mir extension theorem, thereby filling a gap that appears to have remained open in the literature since at least 1985.

To Li and Rui'an

Keywords

$L^2$ extension, $\bar{\partial}$-equation, complete Kähler manifolds, removable singularities, plurisubharmonic functions, complete pluripolar sets

Mathematical Subject Classification

Primary: 32D15, 32D20, 32U05, 32U30

Secondary: 32Q15, 32W05

Milestones

Received: 18 September 2024

Accepted: 2 November 2025

Published: 18 September 2026

Authors

Xieping Wang
CAS Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Sciences University of Science and Technology of China Hefei China

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Vol. 19, No. 7, 2026