Construction of harmonic diffeomorphisms and minimal graphs
نویسندگان
چکیده
We study complete minimal graphs in IH × IR, which take asymptotic boundary values plus and minus infinity on alternating sides of an ideal inscribed polygon Γ in IH. We give necessary and sufficient conditions on the ”lenghts” of the sides of the polygon (and all inscribed polygons in Γ) that ensure the existence of such a graph. We then apply this to construct entire minimal graphs in IH× IR that are conformally the complex plane l C. The vertical projection of such a graph yields a harmonic diffeomorphism from l C onto IH, disproving a conjecture of Rick Schoen. Mathematics Subject Classification: 53A10, 53C43.
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تاریخ انتشار 2017