10 citations · 20 across the 7 of their papers we have counts for
9 papers
Characterization of hyperbolic groups via random walks
Victor Gerasimov, Leonid Potyagailo
Our first result gives a partial converse to a well-known theorem of A. Ancona for hyperbolic groups. We prove that a group , equipped with a symmetric probability measure whose…
Integral criteria of hyperbolicity for graphs and groups
Victor Gerasimov, Leonid Potyagailo
We establish three criteria of hyperbolicity of a graph in terms of ``average width of geodesic bigons''. In particular we prove that if the ratio of the Van Kampen area of a geode…
Martin boundary covers Floyd boundary
Ilya Gekhtman, Victor Gerasimov, Leonid Potyagailo +1
For finitely supported random walks on finitely generated groups we prove that the identity map on extends to a continuous equivariant surjection from the Martin boundary t…
Hausdorff dimension of boundaries of relatively hyperbolic groups
Leonid Potyagailo, Wen-yuan Yang
In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respe…
Similar relatively hyperbolic actions of a group
Victor Gerasimov, Leonid Potyagailo
Let a discrete group possess two convergence actions by homeomorphisms on compacta and . Consider the following question: does there exist a convergence action $G{\curve…
Quasiconvexity in the Relatively Hyperbolic Groups
Victor Gerasimov, Leonid Potyagailo
We study different notions of quasiconvexity for a subgroup of a relatively hyperbolic group The first result establishes equivalent conditions for to be relatively qu…
Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity
Victor Gerasimov, Leonid Potyagailo
The paper consists of two parts. In the first one we show that a relatively hyperbolic group splits as a star graph of groups whose central vertex group is finitely generated a…
On the Complexity and Volume of Hyperbolic 3-Manifolds
Thomas Delzant, Leonid Potyagailo
We compare the volume of a hyperbolic 3-manifold of finite volume and the complexity of its fundamental group.
The boundary of the deformation space of the fundamental group of some hyperbolic 3-manifolds fibering over the circle
Leonid Potyagailo
By using Thurston's bending construction we obtain a sequence of faithful discrete representations ρ_n of the fundamental group of a closed hyperbolic 3-manifold fibering over the…