Harmonic functions of linear growth on solvable groups
Group Theory
2015-10-14 v5 Metric Geometry
Probability
Abstract
In this work we study the structure of finitely generated groups for which a space of harmonic functions with fixed polynomial growth is finite dimensional. It is conjectured that such groups must be virtually nilpotent (the converse direction to Kleiner's theorem). We prove that this is indeed the case for solvable groups. The investigation is partly motivated by Kleiner's proof for Gromov's theorem on groups of polynomial growth.
Cite
@article{arxiv.1408.6243,
title = {Harmonic functions of linear growth on solvable groups},
author = {Tom Meyerovitch and Ariel Yadin},
journal= {arXiv preprint arXiv:1408.6243},
year = {2015}
}