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On the Poisson Integral of Step Functions and Minimal Surfaces

Published online by Cambridge University Press:  20 November 2018

Allen Weitsman
Allen Weitsman*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Inidiana 47907, U.S.A.
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Abstract

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Applications of minimal surface methods are made to obtain information about univalent harmonic mappings. In the case where the mapping arises as the Poisson integral of a step function, lower bounds for the number of zeros of the dilatation are obtained in terms of the geometry of the image.

Keywords

30C6231A0531A2049Q05harmonic mappingsdilatationminimal surfaces

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 154 - 160
Copyright
Copyright © Canadian Mathematical Society 2002

References

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