On the Strong Liouville Property of Covering Spaces
نویسندگان
چکیده
Abstract Lyons and Sullivan conjectured in (J. Differential Geom. 19 (2), 299–323, 1984) that if p : M → N is a normal Riemannian covering, with closed, has exponential volume growth, then there are non-constant, positive harmonic functions on . This was proved recently Polymerakis (Adv. Math. 379 , 107552–107558, 2021) exploiting the Lyons-Sullivan discretization some sophisticated estimates green metric groups. In this note, we provide self-contained proof relying only elementary properties of Brownian motion.
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ژورنال
عنوان ژورنال: Potential Analysis
سال: 2022
ISSN: ['1572-929X', '0926-2601']
DOI: https://doi.org/10.1007/s11118-022-10019-8