Condensers and Equivalent Open Sets on a Riemann Surface

详细

Condensers on the compact closure of an open set on a Riemann surface are studied. The equality of the condenser capacity and module is proved. The definition of NED-sets on a Riemann surface is given, and it is proved that the NED-sets do not affect the condenser module. Also a criterion of equivalence of open sets on a Riemann surface is established.