Optimal constant in an L^2 extension problem and a proof of a conjecture   of Ohsawa
  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. 
Qi'an Guan, Xiangyu Zhou
math.CV math.AG math.DG