On the asymptotic geometry of the hyperbolic plane
Differential Geometry
2007-05-23 v1
Abstract
Asymptotic subcone of an unbounded metric space is another metric space, capturing the structure of the original space at infinity. In this paper we define a functional metric space S which is an asymptotic subcone of the hyperbolic plane. This space is a real tree branching at every its point. Moreover, it is a homogeneous metric space such that any real tree with countably many vertices can be isometrically embedded into it. This implies that every such tree is also an asymptotic subcone of the hyperbolic plane.
Keywords
Cite
@article{arxiv.math/9806106,
title = {On the asymptotic geometry of the hyperbolic plane},
author = {Iosif Polterovich and Alexander Shnirelman},
journal= {arXiv preprint arXiv:math/9806106},
year = {2007}
}
Comments
15 pages, LaTeX