7 citations · 18 across the 8 of their papers we have counts for
8 papers
On horospheric limit sets of Kleinian groups
Kurt Falk, Katsuhiko Matsuzaki
In this paper we partially answer a question of P. Tukia about the size of the difference between the big horospheric limit set and the horospheric limit set of a Kleinian group. W…
Natural maps between CAT(0) boundaries
Stephen M. Buckley, Kurt Falk
It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natur…
The Boundary at Infinity of a rough CAT(0) space
Stephen M. Buckley, Kurt Falk
We develop the boundary theory of rough CAT(0) spaces, a class of spaces that contains both Gromov hyperbolic and CAT(0) spaces. The resulting theory generalizes the common feature…
The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group
Kurt Falk, Katsuhiko Matsuzaki
In this paper we study the relationship between three numerical invariants associated to a Kleinian group, namely the critical exponent, the Hausdorff dimension of the limit set an…
Rough CAT(0) spaces
Stephen M. Buckley, Kurt Falk
We investigate various notions of rough CAT(0). These conditions define classes of spaces that strictly include the union of all Gromov hyperbolic length spaces and all CAT(0) spac…
Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity
Kurt Falk, Bernd O. Stratmann
The main result of this paper is to show that if $\H$ is a normal subgroup of a Kleinian group such that $G/\H$ contains a coset which is represented by some loxodromic element…