Minimal $L^2$ and $L^p$ Ohsawa-Takegoshi extensions

TL;DR

This paper establishes a precise relationship between minimal extensions in $L^2$ and $L^p$ Ohsawa-Takegoshi theorems, providing a new proof for the $L^p$ extension result distinct from previous methods.

Contribution

It introduces a novel connection between $L^2$ and $L^p$ minimal extensions, offering an alternative proof for the $L^p$ Ohsawa-Takegoshi theorem.

Findings

Established a precise relationship between $L^2$ and $L^p$ minimal extensions.

Provided a new proof for the $L^p$ Ohsawa-Takegoshi extension theorem.

Enhanced understanding of extension theorems in complex analysis.

Abstract

We find a precise relationship between the minimal extensions in $L^2$ and $L^p$ Ohsawa-Takegoshi extension theorems. This relationship also gives another proof to the $L^p$ version of the Ohsawa-Takegoshi extension theorem, which is different from the original proof due to Berndtsson-P\u{a}un.