Rough isometries and Dirichlet finite harmonic functions on graphs

Soardi, Paolo M.

doi:10.1090/S0002-9939-1993-1158010-1

Rough isometries and Dirichlet finite harmonic functions on graphs
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Proc. Amer. Math. Soc. 119 (1993), 1239-1248 Request permission

Abstract:

Suppose that ${G_1}$ and ${G_2}$ are roughly isometric connected graphs of bounded degree. If ${G_1}$ has no nonconstant Dirichlet finite harmonic functions, then neither has ${G_2}$.

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