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New examples of harmonic diffeomorphisms of the hyperbolic plane onto itself

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Abstract

A one parameter family of new examples of harmonic maps of the hyperbolic plane onto itself is constructed by studying the Gauss map of certain spacelike constant mean curvature surfaces in three dimensional Minkowski Space. These surfaces are obtained as surfaces of revolution. Explicit construction of the conformal diffeomorphism of the hyperbolic plane onto such surfaces gives a complete description of the boundary behavior of the harmonic maps.

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, 52242, Iowa City, Iowa

    Hyeong In Choi & Andrejs Treibergs

  2. Department of Mathematics, University of Utah, 84112, Salt Lake City, Utah

    Hyeong In Choi & Andrejs Treibergs

Authors
  1. Hyeong In Choi
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  2. Andrejs Treibergs
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Additional information

Partially supported by N. S. F. grant NSF-DMS8503327

Partially supported by N. S. F. grant NSF-DMS8700783

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Choi, H.I., Treibergs, A. New examples of harmonic diffeomorphisms of the hyperbolic plane onto itself. Manuscripta Math 62, 249–256 (1988). https://doi.org/10.1007/BF01278983

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  • DOI: https://doi.org/10.1007/BF01278983

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