Harmonic Splittings of Surfaces

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dc.creatorFarb, Benson
dc.creatorWolf, Michael
dc.date2000-03-08
dc.date.accessioned2026-07-07T04:34:14Z
dc.date.available2026-07-07T04:34:14Z
dc.descriptionWe give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal G-action on a real tree is dual to the lift of a measured foliation. Analytic tools like the maximum principle are used to simplify the usual combinatorial topology arguments. Other analytic objects associated to a harmonic map, such as the Hopf differential and the moduli space of harmonic maps, are also introduced as tools for understanding the action of surface groups on trees.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0003051
dc.identifierhttp://arxiv.org/abs/math/0003051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58828
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.titleHarmonic Splittings of Surfaces
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