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arXiv · 2004.14624

An embedding of the Morse boundary in the Martin boundary

Matthew Cordes·Matthieu Dussaule·Ilya Gekhtman
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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.

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Matthew Cordes, Matthieu Dussaule, Ilya Gekhtman. 2020-04-30. An embedding of the Morse boundary in the Martin boundary. https://doi.org/10.2140/agt.2022.22.1217

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