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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.

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C43 Differential geometric aspects of harmonic maps
Full Text: DOI
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