Horofunctions on graphs of linear growth

Abstract

We prove that a linear growth graph has finitely many horofunctions. This provides a short and simple proof that any finitely generated infinite group of linear growth is virtually cyclic.

arXiv comment4 pages. Published in C. R. Math. Acad. Sci. Paris at http://www.sciencedirect.com/science/article/pii/S1631073X16302060