For any open Riemann surface $X$ admitting Green functions, Suita asked about the precise relations between the Bergman kernel and the logarithmic capacity. It was conjectured that the Gaussian curvature of the Suita metric is bounded from above by $-4$, and moreover the curvature is equal to $-4$ at some point if and only if $X$ is conformally equivalent to the unit disc less a (possible) closed polar subset. After the contributions made by B{\l}ocki, Guan & Zhou and Berndtsson & Lempert, we provide a new proof of the equality part in Suita's conjecture by using the plurisubharmonic variation properties of Bergman kernels. 查看全文>>