A simplified proof of optimal $L^2$-extension theorem and extensions from non-reduced subvarieties

TL;DR

This paper presents a simplified proof of the optimal $L^2$-extension theorem, improving understanding and providing optimal estimates for extensions from non-reduced subvarieties using variational methods.

Contribution

It offers a simplified, optimal proof of the $L^2$-extension theorem and extends the results to non-reduced subvarieties with precise estimates.

Findings

Simplified proof of the optimal $L^2$-extension theorem

Optimal estimates for extensions from non-reduced subvarieties

Application of variational methods in extension problems

Abstract

We give a simplified proof of an optimal version of the Ohsawa-Takegoshi $L^2$-extension theorem. We follow the variational proof by Berndtsson-Lempert and use the method in the paper of McNeal-Varolin. As an application, we give an optimal estimate for extensions from possibly non-reduced subvarieties.