An extremal problem for Dirichlet-finite holomorphic functions on Riemann surfaces
Let R be a Riemann surface, f a nonconstant holomorphic function on R with finite Dirichlet integral D(f), and \(f_ 2\) the least harmonic majorant of f. Theorem: \(\pi\) \(\sum f_ 2(a)\leq D(f)\), the sum over all a for which \(f(a)=0\). Conditions for equality are given.
scientific article; zbMATH DE number 3920910