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.
Original language | English |
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Pages (from-to) | 149-180 |
Number of pages | 32 |
Journal | Israel Journal of Mathematics |
Volume | 216 |
Issue number | 1 |
DOIs | |
State | Published - 1 Oct 2016 |
ASJC Scopus subject areas
- General Mathematics