Suita conjecture and the Ohsawa-Takegoshi extension theorem

We prove a conjecture of N. Suita which says that for any bounded domain D in ? one has $c_{D}^{2}\leq\pi K_{D}$ , where c _D (z) is the logarithmic capacity of ??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.