An embedding of the Morse boundary in the Martin boundary

Matthew Cordes, Matthieu Dussaule, Ilya Gekhtman

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1217-1253
Number of pages37
JournalAlgebraic and Geometric Topology
Issue number3
Publication statusPublished - 25 Aug 2022


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