On harmonic functions and the linear-growth case of Gromov's theorem
Group Theory
2013-11-20 v3 Combinatorics
Metric Geometry
Abstract
We show that the space of harmonic functions on a finitely generated infinite group G is finite dimensional if, and only if, G has a finite-index subgroup isomorphic to the integers. A key tool is Wilkie and van den Dries's quantitative version of the linear-growth case of Gromov's theorem on groups of polynomial growth.
Keywords
Cite
@article{arxiv.1301.1566,
title = {On harmonic functions and the linear-growth case of Gromov's theorem},
author = {Matthew Tointon},
journal= {arXiv preprint arXiv:1301.1566},
year = {2013}
}
Comments
This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 3.3. This came to light after an observation made by an anonymous referee, for which the the author is grateful