Mitra, Mahan (1998) Cannon-Thurston maps for trees of hyperbolic metric spaces Journal of Differential Geometry, 48 . pp. 135-164. ISSN 0022-040X
![]()
|
PDF
- Author Version
258kB |
Official URL: http://arxiv.org/pdf/math/9609209.pdf
Abstract
Let (X,d) be a tree (T) of hyperbolic metric spaces satisfying the quasi-isometrically embedded condition. Let v be a vertex of T . Let (Xv, dv) denote the hyperbolic metric space corresponding to v. Then i : Xv → X extends continuously to a map i^ : X^v → X^. This generalizes a Theorem of Cannon and Thurston. The techniques are used to give a new proof of a result of Minsky: Thurston's ending lamination conjecture for certain Kleinian groups. Applications to graphs of hyperbolic groups and local connectivity of limit sets of Kleinian groups are also given.
Item Type: | Article |
---|---|
Source: | Copyright of this article belongs to International Press. |
ID Code: | 89547 |
Deposited On: | 28 Apr 2012 12:55 |
Last Modified: | 19 May 2016 04:04 |
Repository Staff Only: item control page