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VOL. 57 | 2010 Functions of finite Dirichlet sums and compactifications of infinite graphs
Tae Hattori, Atsushi Kasue

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai

## Abstract

We introduce the $p$-resister for an infinite network and show a comparison theorem on the resisters for two infinite graphs of bounded degrees which are quasi isometric. Some geometric projections of the Royden $p$-compactifications of infinite networks are investigated and several observations are made in relation to geometric boundaries of hyperbolic networks in the sense of Gromov. In addition, a Riemannian manifold which is quasi isometric to the hyperbolic space form is constructed to illustrate a role of the bounded local geometry in studying points at infinity.

## Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1203.53033
MathSciNet: MR2648257

Digital Object Identifier: 10.2969/aspm/05710141

Subjects:
Primary: 53C21, 58D17, 58J50