The support of an extremal dilatation

Marvin E. Ortel

Vol. 99 (1982), No. 2, 431–438

DOI: 10.2140/pjm.1982.99.431

Abstract

We introduce a density condition which applies to subsets, E, of a bounded region Ω in the complex plane. If E satisfies this condition, then it is possible to construct a quasiconformal mapping F, of Ω, subject to the following conditions: F is extremal for its boundary values; F is conformal throughout Ω − E; F is not conformal on E. The construction makes essential use of the Hamilton-Reich-Strebel characterization of extremal quasiconformal maps.

Mathematical Subject Classification

Primary: 30C60, 30C60

Milestones

Received: 12 July 1979

Published: 1 April 1982