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math.GR2026
On Uniformly Perfect Morse Boundaries
Suzhen Han, Qing Liu
We introduce and geometrically characterize the notion of uniformly perfect Morse boundary for proper geodesic metric spaces. As a unifying result, we prove that the Morse boundary…
math.GR2024
Growth Rate Gap for Stable Subgroups
Suzhen Han, Qing Liu
We prove that stable subgroups of Morse local-to-global groups exhibit a growth gap. That is, the growth rate of an infinite-index stable subgroup is strictly less than the growth…