Harmonic functions of linear growth on solvable groups

Tom Meyerovitch; Ariel Yadin

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arXiv · 1408.6243

Harmonic functions of linear growth on solvable groups

Tom Meyerovitch·Ariel Yadin

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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.

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BibTeX RIS

Tom Meyerovitch, Ariel Yadin. 2014-08-26. Harmonic functions of linear growth on solvable groups. https://arxiv.org/abs/1408.6243

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