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A COUNTEREXAMPLE TO UNIQUENESS IN THE RIEMANN MAPPING THEOREM FOR UNIVALENT HARMONIC MAPPINGS

Published online by Cambridge University Press:  01 January 1999

ALLEN WEITSMAN
ALLEN WEITSMAN
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
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Abstract

Let f be an orientation-preserving univalent harmonic mapping of the unit disk U. Then f=h+[gmacron], where h and g are analytic in U. Furthermore, f satisfies the equation

formula here

in U, where a(z)=g′(z)/h′(z), and [mid ]a(z)[mid ]<1 in U. The function a(z) is the analytic dilatation of f.

In [2], Hengartner and Schober proved the following version of the Riemann mapping theorem for univalent harmonic mappings.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 1 , January 1999 , pp. 87 - 89
Copyright
© The London Mathematical Society 1999

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