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

TL;DR

This paper establishes optimal $L^2$ extension theorems for holomorphic sections from subvarieties in weakly pseudoconvex Kähler manifolds, including cases with singular Hermitian metrics on line bundles.

Contribution

It provides the first optimal $L^2$ extension results in weakly pseudoconvex Kähler manifolds, allowing singular metrics for line bundles.

Findings

Optimal $L^2$ extension from subvarieties achieved

Extension results hold for singular Hermitian metrics

Advances in extension theory in complex geometry

Abstract

In this paper, we obtain optimal $L^2$ extension of holomorphic sections of a holomorphic vector bundle from subvarieties in weakly pseudoconvex K\"{a}hler manifolds. Moreover, in the case of line bundle the Hermitian metric is allowed to be singular.