Optimal constant in an L^2 extension problem and a proof of a conjecture of Ohsawa

TL;DR

This paper determines the optimal constant in an L^2 extension theorem, proving a conjecture by Ohsawa and the extended Suita conjecture, and explores relations between Bergman kernel and capacity on Riemann surfaces.

Contribution

It provides the exact optimal constant for Ohsawa's L^2 extension theorem and proves significant conjectures in complex analysis.

Findings

Solved the optimal constant problem in L^2 extension theorem

Proved Ohsawa's conjecture and the extended Suita conjecture

Established relations between Bergman kernel and logarithmic capacity

Abstract

In this paper, we solve the optimal constant problem in the setting of Ohsawa's generalized $L^{2}$ extension theorem. As applications, we prove a conjecture of Ohsawa and the extended Suita conjecture, we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.