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Construction of harmonic diffeomorphisms and minimal graphs. (English) Zbl 1209.53010
The paper constructs harmonic diffeomorphisms from $$\mathbb C$$ onto $$\mathbb H$$. The authors use entire minimal graphs to construct such examples. The constructions are used within a general study of complete minimal graphs in $$\mathbb H \times \mathbb R$$, which take asymptotic boundary values plus and minus infinity on alternating sides of an ideal inscribed polygon in $$\mathbb H$$. A diffeomorphism from $$\mathbb C$$ onto $$\mathbb H$$ is constructed based on a certain entire minimal graph $$\mathbb H \times \mathbb R$$, which disproves a conjecture of Schoen and Yau.

##### MSC:
 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53C43 Differential geometric aspects of harmonic maps
##### Keywords:
minimal surfaces; minimal graphs; harmonic maps
Full Text:
##### References:
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