3 papers
math.GR2026
Harmonic projection and hypercentral extensions
Antoine Gournay
The Liouville property is a strong form of amenability, but contrary to amenability, it is not well-behaved under extensions. In this paper it is shown that, for some measures, the…
math.GR2025
Radial isoperimetry and absence of harmonic functions with -gradient
Antoine Gournay
In this paper we show that groups for which the probability of return of a random walk is bounded below by have no non-constant harmonic functions with gradient…
math.GR2024
Regular maps from the lamplighter to metabelian groups
Antoine Gournay, Corentin Le Coz
We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group which is not virtually nilpotent. This implies that finitely genera…