Construction of harmonic diffeomorphisms and minimal graphs

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dc.creatorCollin, Pascal
dc.creatorRosenberg, Harold
dc.date2007-01-19
dc.date.accessioned2026-07-07T07:41:57Z
dc.date.available2026-07-07T07:41:57Z
dc.descriptionWe study complete minimal graphs in HxR, which take asymptotic boundary values plus and minus infinity on alternating sides of an ideal inscribed polygon Γ in H. 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 HxR that are conformally the complex plane C. The vertical projection of such a graph yields a harmonic diffeomorphism from C onto H, disproving a conjecture of Rick Schoen.
dc.identifierhttps://arxiv.org/abs/math/0701547
dc.identifierhttp://arxiv.org/abs/math/0701547
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122309
dc.subjectDifferential Geometry
dc.subjectMSC: 53A10, 53C43
dc.titleConstruction of harmonic diffeomorphisms and minimal graphs
dc.typetext

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