Weighted Modules and Capacities on a Riemann Surface

Аннотация

On a Riemann surface (in the broad sense of the word in the terminology of Hurwitz–Courant), the weighted capacity and module (with a Muckenhoupt weight) of a condenser with a finite number of plates are defined. The equality of the capacity and module of a condenser is proved, which solves a Dubinin problem.