Harmonic Functions on Compactly Generated Groups

2020/12/14 by Creutz, Darren
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2012.07948

Abstract

A compactly generated group is noncompact if and only if it admits a nonconstant harmonic function (for some, equivalently for every, reasonable measure). This generalizes the known fact that a finitely generated group is infinite if and only if it admits a nonconstant harmonic function (for some, equivalently every, reasonable measure).

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