A Remark on Optimal $L^2$ extension theorem for holomorphic vector bundles

TL;DR

This paper establishes a unified optimal $L^2$ extension theorem for holomorphic vector bundles with smooth hermitian metrics on weakly pseudoconvex Kähler manifolds, generalizing previous results by Guan-Zhou and Zhou-Zhu.

Contribution

It provides a unified and optimal $L^2$ extension theorem for holomorphic vector bundles, extending previous theorems to a broader setting with continuous gain.

Findings

Unified version of $L^2$ extension theorems

Applicable to weakly pseudoconvex Kähler manifolds

Generalizes prior results by Guan-Zhou and Zhou-Zhu

Abstract

In this note, we present an optimal $L^2$ extension theorem for holomorphic vector bundles with smooth hermitian metrics for continuous gain on weakly pseudoconvex K\"{a}hler manifolds, which is a unified version of the optimal $L^2$ extension theorems for holomorphic vector bundles with smooth hermitian metrics of Guan-Zhou and Zhou-Zhu.