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

MSC:
53A10Minimal surfaces, surfaces with prescribed mean curvature
53C43Differential geometric aspects of harmonic maps