Generalized Reduced Module of a Domain Over the Unit Disc with Circular and Radial Slits

Abstract

For (n + 1)-ly connected planar domain D with analytic boundary we construct the function F(w,w₀) = (w − w₀)f(w,w₀) which maps D conformally onto the unit disk with circular and radial slits. We show that if n ≥ 2, then Mityuk’s function, M(w) = −(2π)⁻¹ ln |f(w,w)|, representing the generalized reduced module of the domain D has at least one stationary point in D.