Harmonic Functions on Compactly Generated Groups
Group Theory
2022-01-13 v3
Abstract
A compactly generated group is noncompact if and only if it admits a nonconstant harmonic function (for some, equivalently for every, reasonable measure). This generalizes the known fact that a finitely generated group is infinite if and only if it admits a nonconstant harmonic function (for some, equivalently every, reasonable measure).
Cite
@article{arxiv.2012.07948,
title = {Harmonic Functions on Compactly Generated Groups},
author = {Darren Creutz},
journal= {arXiv preprint arXiv:2012.07948},
year = {2022}
}