Harmonic functions of linear growth on solvable groups

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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.

Original languageEnglish
Pages (from-to)149-180
Number of pages32
JournalIsrael Journal of Mathematics
Volume216
Issue number1
DOIs
StatePublished - 1 Oct 2016

ASJC Scopus subject areas

  • Mathematics (all)

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