On sharper estimates of Ohsawa-Takegoshi $L^2$-extension theorem

TL;DR

This paper introduces a new $L^2$-extension theorem with sharper estimates based on weight functions, improving upon existing bounds especially for strictly pseudoconvex Hartogs domains and radial weights, achieving minimal extensions.

Contribution

The authors develop a sharper $L^2$-extension estimate that depends on weight functions, surpassing previous optimal bounds in specific geometric settings.

Findings

Sharper estimates for strictly pseudoconvex Hartogs domains

Extension achieves $L^2$-minimum in radial weight cases

Improves upon known optimal $L^2$-extension bounds

Abstract

We present an $L^2$-extension theorem with an estimate depending on the weight functions for domains in $\mathbb{C}$. When the Hartogs domain defined by the weight function is strictly pseudoconvex, this estimate is strictly sharper than known optimal estimates. When the weight function is radial, we prove that our estimate provides the $L^2$-minimum extension.