An optimal $L^2$ extension for continuous $L^2$-optimal Hermitian metrics

TL;DR

This paper establishes an optimal $L^2$ extension theorem for continuous $L^2$-optimal Hermitian metrics on bounded planar domains, providing solutions to existing open questions in the field.

Contribution

It introduces a new optimal $L^2$ extension theorem for Hermitian metrics, advancing the understanding of $L^2$ extension problems in complex analysis.

Findings

Proves an optimal $L^2$ extension theorem for continuous $L^2$-optimal Hermitian metrics.

Answers affirmatively to questions posed by Deng-Ning-Wang and Inayama.

Enhances the theoretical framework for $L^2$ extension in complex geometry.

Abstract

In this paper, we obtain an optimal $L^2$ extension theorem for continuous $L^2$-optimal Hermitian metric on bounded planer domains. As applications, we affirmatively answer a question of Deng-Ning-Wang and a question of Inayama.