On the conformal mapping of variable regions

Abstract

We establish an estimate for the functional ίώl, Kf,g;p)=\ \M-g(t)\.Cp is the circumference \t \ = p, 0 ^ p < 1.Here / and g are normalized conformal mapping functions of | z \ < 1 onto a pair of bounded, open, simply connected, origin containing domains in the w plane whose boundaries are near each other in some sense.In the second part of the paper we establish an estimate for the functional /(/', g'; p) in case the boundaries are additionally assumed to be rectifiable.

Locations

• Pacific Journal of Mathematics - View - PDF