Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

On the strong Liouville property of covering spaces


Polymerakis,  Panagiotis
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

Polymerakis, P. (in press). On the strong Liouville property of covering spaces. Potential Analysis, Published Online - Print pending. doi:10.1007/s11118-022-10019-8.

Cite as: https://hdl.handle.net/21.11116/0000-000A-AC9D-4
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.