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1 Laboratoire de Mathématiques de Neuchâtel

Abstract : We obtain a new result concerning harmonic functions on infinite Cayley graphs $X$: either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of $X$. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology are also discussed.

Keywords : Discrete random walks Dirichlet problem radial variation hyperbolic compactifications





Author: Anders Karlsson -

Source: https://hal.archives-ouvertes.fr/



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