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An embedding of the Morse boundary in the Martin boundary

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arxiv 2004.14624 v2 pith:T3EA5DL2 submitted 2020-04-30 math.GR math.MGmath.PR

Matthew Cordes (D-MATH) , Matthieu Dussaule (LMJL) , Ilya Gekhtman This is my paper · ORCID
classification math.GRmath.MGmath.PR
keywords boundarymorsehyperbolicgroupgroupsmartinmeasureancona
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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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