Some remarks on harmonic functions on homogeneous graphs
نویسنده
چکیده
We obtain a new result concerning harmonic functions on Cayley graphs X: either every nonconstant harmonic function has large radial variation (in a certain sense), or there is a nontrivial hyperbolic boundary 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.
منابع مشابه
Some remarks concerning harmonic functions on homogeneous graphs
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. C...
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