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arXiv · 1301.1566

On harmonic functions and the linear-growth case of Gromov's theorem

Matthew Tointon
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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.

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Matthew Tointon. 2013-11-18. On harmonic functions and the linear-growth case of Gromov's theorem. https://arxiv.org/abs/1301.1566

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