All Questions
4 questions with no upvoted or accepted answers
6
votes
0
answers
383
views
When is a word metric on a CAT(-1) group a bounded distance from the orbit map of an isometric action on some CAT(-k) metric space?
Let $\Gamma$ be a group admitting a discrete and cocompact action on a CAT(-1) space.
Let $d$ a word metric on $\Gamma$ coming from some finite set of generators.
My question is:
Does there exist a ...
- 2,964
5
votes
0
answers
155
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Are there examples of hyperbolic manifolds with finite Bowen-Margulis measure and fundamental group which is not relatively hyperbolic?
It is well known that a geometrically finite hyperbolic manifold (quotient of $H^n$) has finite Bowen-Margulis measure.
Marc Peigné [1] constructed examples of geometrically infinite hyperbolic ...
- 481
3
votes
0
answers
99
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Relation of geometric and polyhedral convergence
By Proposition 3.10(i) of Jorgensen and Marden's 1990 Algebraic and geometric convergence of Kleinian groups, "[A] sequence $\{G_n\}$ of Kleinian groups converges geometrically to a Kleinian ...
- 61
2
votes
0
answers
87
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Hausdorff dimension of radial limit sets for divergence type subgroups
Let $X$ be a proper $CAT(-1)$ space.
Let $\Gamma<Isom(X)$ be a subgroup of divergence type.
Is it true that the Hausdorff dimension of the radial limit set of $\Gamma$ in $\partial X$ is equal to ...
- 2,964