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Rough isometries and Dirichlet finite harmonic functions on graphs

Author: Paolo M. Soardi
Journal: Proc. Amer. Math. Soc. 119 (1993), 1239-1248
MSC: Primary 31C05; Secondary 94C05
MathSciNet review: 1158010
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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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Keywords: Rough isometries, infinite networks, infinite graphs, Dirichlet finite harmonic functions
Article copyright: © Copyright 1993 American Mathematical Society

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