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On the Poisson Integral of Step Functions and Minimal Surfaces |
Published:2002-03-01
Printed: Mar 2002
Printed: Mar 2002
- Allen Weitsman
Abstract
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: | harmonic mappings, dilatation, minimal surfaces |
| MSC Classifications: |
30C62 - Quasiconformal mappings in the plane 31A05 - Harmonic, subharmonic, superharmonic functions 31A20 - Boundary behavior (theorems of Fatou type, etc.) 49Q05 - Minimal surfaces [See also 53A10, 58E12] |