Bridged extremal distance and maximal capacity
We introduce the concept of ``bridged extremal distance'' between subsets \(X\) and \(Z\) lying on the boundary of a finitely-connected domain \(G\) -- that is, the extremal length of the family of curves connecting \(X\) and \(Z\) which are allowed to stop at a component of the ``bridge'' \(Y= \partial G\setminus (X \cup Z)\) and re-emerge from any other point of that component. We identify bridged extremal distance with the extremal problem of ``minimal extremal distance'', and express it in terms of the period matrix associated with the harmonic measures of the boundary components of \(G\). We then use bridged extremal distance to give an extremal length interpretation of ``maximal capacity'', via ``reduced extremal distance''.
scientific article; zbMATH DE number 950230