Proceedings of the American Mathematical Society

Author(s): Gábor Elek; Gábor Tardos
Journal: Proc. Amer. Math. Soc. 128 (2000), 2479-2485.
MSC (1991): Primary 58G05
Posted: February 25, 2000
Retrieve article in: PDF
This article is available free of charge

We introduce the notion of rough transitivity and prove that there exist no non-constant harmonic Dirichlet functions on amenable roughly transitive graphs.

1.: I. BENJAMINI, R. LYONS, Y. PERES, and O. SCHRAMM, Uniform spanning forests, preprint, 1998.
2.: J. CHEEGER and M. GROMOV, -cohomology and group cohomology, Topology 25 (1986), 189-215. MR 87i:58161
3.: G. ELEK, On the Cayley graph of an amenable group, Acta Mathematica Hungarica 74 (1997), no. 3, 229-234. MR 98d:46078
4.: A. MALCEV, On a class of homogeneous spaces, AMS Translations 39 (1951). MR 12:589e
5.: G. MEDOLLA and P. M. SOARDI, Extension of Foster's averaging formula to infinite networks with moderate growth, Math. Z. 219 (1995), 171-185. MR 96g:94031
6.: P. PANSU, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Annals of Math. 129 (1989), 1-60. MR 90e:53058
7.: W. PASCHKE, An invariant for finitely presented -modules, Math. Ann. 301 (1995), no. 2, 325-337. MR 96k:20009
8.: J. SCHEUNEMAN, Two-Step Nilpotent Lie Algebras, Journal of Algebra 7 October (1967), 152-159. MR 36:225
9.: P. M. SOARDI, Rough isometries and Dirichlet finite harmonic functions on graphs, Proc. of the AMS 119 (1993) , 1239-1248. MR 94a:31004
10.: P. M. SOARDI, Potential theory of infinite networks, Lecture notes in Mathematics 1590 (1994). MR 96i:31005
11.: V.I. TROFIMOV, Graphs with polynomial growth, Math. Sbornik 51 (1985). MR 85m:05041

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58G05

Gábor Elek
Affiliation: Rényi Institute of the Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary
Email: elek@math-inst.hu

Gábor Tardos
Affiliation: Rényi Institute of the Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary
Email: tardos@math-inst.hu

DOI: 10.1090/S0002-9939-00-05288-6
PII: S 0002-9939(00)05288-6
Keywords: Amenable graphs, harmonic functions
Received by editor(s): July 6, 1998
Received by editor(s) in revised form: September 8, 1998
Posted: February 25, 2000
Additional Notes: The first author was supported by OTKA grant T25004 and the Bolyai Fellowship.
The second author was supported by OTKA grants F014919, T029255 and AKP grant 97-56.
Communicated by: Józef Dodziuk
Copyright of article: Copyright 2000, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS