Boundary behaviour of harmonic functions on hyperbolic groups

Details Boundary behaviour of harmonic functions on hyperbolic groups Boundary behaviour of harmonic functions on hyperbolic groups

2009-05-26

arxiv.org/abs/0905.4118v1

Mathematics

Metric Geometry

12 pages

Scientific paper

We consider random walks with finite support on non-elementary Gromov hyperbolic groups. For a given harmonic function on such a group, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The proof is inspired from works of F. Mouton in the cases of Riemannian manifolds of pinched negative curvature and infinite trees. It involves geometric and probabilitistic methods.

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