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arXiv · 2012.07948

Harmonic Functions on Compactly Generated Groups

Darren Creutz
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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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Darren Creutz. 2020-12-14. Harmonic Functions on Compactly Generated Groups. https://arxiv.org/abs/2012.07948

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