Abstract

AbstractIn this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space ofp-Dirichlet finite functions on connected infinite graphs, via quasi-monomorphisms. A main result shows that if a connected infinite graph of bounded degrees possesses a quasi-monomorphism into the hyperbolic space form of dimensionnand it is notp-parabolic forp > n -1, then it admits a lot ofp-harmonic functions with finite Dirichlet sum of orderp.

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