On harmonic functions and the linear-growth case of Gromov's theorem
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🧮 math.GR
math.COmath.MG
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casefunctionsgromovharmoniclinear-growththeoremdimensionaldries
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We show that the space of harmonic functions on a finitely generated infinite group G is finite dimensional if, and only if, G has a finite-index subgroup isomorphic to the integers. A key tool is Wilkie and van den Dries's quantitative version of the linear-growth case of Gromov's theorem on groups of polynomial growth.
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