Abstract For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, logarithmic capacity $c_{\beta }$, and analytic $c_{B}$ satisfy inequality chain $\pi K \geq c^2_{\beta } c^2_B$. Moreover, equality holds at a single point between two of three quantities if only $X$ is biholomorphic to disk possibly less relatively closed polar set. We extend by showing that $c_{B}^2 \pi v^{-1}(X)$ ...
