The Martin boundary of an extension by a hyperbolic group

We prove uniform Ancona—Gouëzel—Lalley inequalities for an extension by a hyperbolic group G of Markov map which allows to deduce that the visual boundary and Martin are Hölder equivalent. As application, we identify set minimal δ-conformal measures regular cover convex-cocompact CAT(-1)-manifold with covering group, provided this is hyperbolic. In setting, uniformity minimal, densities in sense Patterson respect exponent convergence δ. This interest as δ coincides Hausdorff dimension radial limit set. Moreover, extends Roblin’s identification s-conformal s >