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On the Poisson Integral of Step Functions and Minimal Surfaces

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

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