English

The Martin boundary of an extension by a hyperbolic group

Dynamical Systems 2024-03-28 v1

Abstract

We prove uniform Ancona-Gou\"ezel-Lalley inequalities for an extension by a hyperbolic group GG of a Markov map which allows to deduce that the visual boundary of the group and the Martin boundary are H\"older equivalent. As application, we identify the set of minimal conformal measures of a regular cover of a convex-cocompact CAT(-1)-manifold with the visual boundary of the covering group, provided that this group is hyperbolic.

Keywords

Cite

@article{arxiv.2005.03723,
  title  = {The Martin boundary of an extension by a hyperbolic group},
  author = {Sara Ruth Pires Bispo and Manuel Stadlbauer},
  journal= {arXiv preprint arXiv:2005.03723},
  year   = {2024}
}