Explicit constructions of universal R-trees and asymptotic geometry of hyperbolic spaces

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dc.creatorDyubina, Anna
dc.creatorPolterovich, Iosif
dc.date1999-04-23
dc.date2000-04-04
dc.date.accessioned2026-07-07T05:28:48Z
dc.date.available2026-07-07T05:28:48Z
dc.descriptionWe present some explicit constructions of universal R-trees with applications to the asymptotic geometry of hyperbolic spaces. In particular, we show that any asymptotic cone of a complete simply connected manifold of negative curvature is a complete homogeneous R-tree with the valency $2^{\aleph_0}$ at every point. It implies that all these asymptotic cones are isometric depending neither on a manifold nor on an ultrafilter. It is also proved that the same R-tree can be isometrically embedded at infinity into such a manifold or into a non-abelian free group.
dc.descriptionRevised version
dc.identifierhttps://arxiv.org/abs/math/9904133
dc.identifierhttp://arxiv.org/abs/math/9904133
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78397
dc.subjectDifferential Geometry
dc.subjectGroup Theory
dc.subject53Cxx, 20F32
dc.titleExplicit constructions of universal R-trees and asymptotic geometry of hyperbolic spaces
dc.typetext

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