Rough isometries and Dirichlet finite harmonic functions on graphs

Paolo M. Soardi
1993 Proceedings of the American Mathematical Society  
Suppose that G\ and G% are roughly isometric connected graphs of bounded degree. If G\ has no nonconstant Dirichlet finite harmonic functions, then neither has Gi.
doi:10.1090/s0002-9939-1993-1158010-1 fatcat:74ao4swtxnhvfcwjivtlckxbvi