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- W4283067716 abstract "Abstract Lyons and Sullivan conjectured in Lyons and Sullivan (J. Differential Geom. 19 (2), 299–323, 1984) that if p : M → N is a normal Riemannian covering, with N closed, and M has exponential volume growth, then there are non-constant, positive harmonic functions on M . This was proved recently in Polymerakis (Adv. Math. 379 , 107552–107558, 2021) exploiting the Lyons-Sullivan discretization and some sophisticated estimates on the green metric on groups. In this note, we provide a self-contained proof relying only on elementary properties of the Brownian motion." @default.
- W4283067716 created "2022-06-19" @default.
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- W4283067716 date "2022-06-18" @default.
- W4283067716 modified "2023-10-09" @default.
- W4283067716 title "On the Strong Liouville Property of Covering Spaces" @default.
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- W4283067716 doi "https://doi.org/10.1007/s11118-022-10019-8" @default.
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