The optimal jet $L^2$ extension of Ohsawa-Takegoshi type

TL;DR

This paper proves an optimal $L^2$ extension theorem for jets, utilizing Hermitian metrics on jet bundles and building on the methods of Berndtsson-Lempert and Demailly.

Contribution

It introduces an optimal $L^2$ extension result for jets, advancing the understanding of extension theorems with precise estimates.

Findings

Established an $L^2$ extension theorem for jets with optimal estimates

Utilized Hermitian metrics on jet bundles following Demailly's construction

Extended the method of Berndtsson-Lempert to jet extension problems

Abstract

We prove the $L^2$ extension theorem for jets with optimal estimate following the method of Berndtsson-Lempert. For this purpose, following Demailly's construction, we consider Hermitian metrics on jet vector bundles.