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

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We 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.
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Differential Geometry, Group Theory, 53Cxx, 20F32

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http://salesiana.dossiersoluciones.com/handle/123456789/78397

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9904133
 http://arxiv.org/abs/math/9904133

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arXiv