Suita conjecture and the Ohsawa-Takegoshi extension theorem

Abstract

We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has cD2 ≤ π KD, where c D(z) is the logarithmic capacity of ℂ{set minus}D with respect to z∈D and K D the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem. © 2012 The Author(s).