An embedding of the Morse boundary in the Martin boundary
Group Theory
2022-09-07 v2 Metric Geometry
Probability
Abstract
We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.
Keywords
Cite
@article{arxiv.2004.14624,
title = {An embedding of the Morse boundary in the Martin boundary},
author = {Matthew Cordes and Matthieu Dussaule and Ilya Gekhtman},
journal= {arXiv preprint arXiv:2004.14624},
year = {2022}
}