Suppose that G1 and G2 are roughly isometric connected graphs of bounded degree. If G1 has nonconstant Dirichlet finite harmonic functions, then neither has G2
Soardi, P. (1993). Rough isometries and Dirichlet finite harmonic functions on graphs. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 119(4), 1239-1248 [10.1090/S0002-9939-1993-1158010-1].
Rough isometries and Dirichlet finite harmonic functions on graphs
SOARDI, PAOLO MAURIZIO
1993
Abstract
Suppose that G1 and G2 are roughly isometric connected graphs of bounded degree. If G1 has nonconstant Dirichlet finite harmonic functions, then neither has G2
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