On the asymptotic geometry of the hyperbolic plane

Details On the asymptotic geometry of the hyperbolic plane On the asymptotic geometry of the hyperbolic plane

1998-06-19

arxiv.org/abs/math/9806106v1

Mathematics

Differential Geometry

15 pages, LaTeX

Scientific paper

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.

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