Anders Karlsson - Some remarks concerning harmonic functions on homogeneous graphs

dmtcs:3348 - Discrete Mathematics & Theoretical Computer Science, January 1, 2003, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) - https://doi.org/10.46298/dmtcs.3348
Some remarks concerning harmonic functions on homogeneous graphs

Authors: Anders Karlsson

    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.


    Volume: DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
    Section: Proceedings
    Published on: January 1, 2003
    Imported on: May 10, 2017
    Keywords: Discrete random walks,Dirichlet problem,radial variation,hyperbolic compactifications,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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