ON THE EXISTENCE OF CERTAIN GENERAL EXTREMAL METRICS-II

The author was the first to show the important role played by quadrati c differentials all of whose structure domains are ring domains manife sting in particular their relation to module problems for multiple cur ve families and the related problems for linear sums of modules of dou ble-connected domains. The original method used variational techniques . In this paper a treatment is given using directly the method of the extremal metric.