Vol. 34, No. 1, 1970

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ISSN: 0030-8730
On the conformal mapping of variable regions

Frank J. Polansky

Vol. 34 (1970), No. 1, 145–155
Abstract

We establish an estimate for the functional

I(f,g;ρ) =!cρ|f(t)− g(t)|⋅|dt|,

Cρ is the circumference |t| = ρ,0 ρ < 1. Here f 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 I(f,g;p) in case the boundaries are additionally assumed to be rectifiable.

Mathematical Subject Classification
Primary: 30.40
Milestones
Received: 12 February 1968
Published: 1 July 1970
Authors
Frank J. Polansky