A non-standard integral equation with applications to quasiconformal mappings

Abstract

A) Let C denote an oriented closed Jordan curve in the extended complex plane (Riemann sphere). We denote by DI=DI(C ) and D2=D2(C ) the domains interior and exterior to C, respectively, and we denote by 2~(z) ldz I =~Dj(C)(z)ldz ] the Poincar4 metric in D~, ?'=1, 2. We denote by q an integer, q~>2.