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Zbl 1005.31005
Blachère, Sébastien
Harmonic functions on annuli of graphs. (English)
[J] Ann. Math. Blaise Pascal 8, No.2, 47-59 (2001). ISSN 1259-1734

The author proves the ``relative connectedness'' of graphs which satisfy a polynomial volume growth and a Poincaré-type inequality on balls. By ``relative connectedness'' it is meant that every two vertices at distance $R$ from a vertex $x$ can be joined by a path within an annulus. In the case of Cayley graph of groups having polynomial volume growth, the above result uses to obtain a Poincaré-type inequality on the annuli.
[Sophia L.Kalpazidou (Thessaloniki)]

MSC 2000:: *31C20 Discrete potential theory, etc.
05C40 Connectivity

Keywords: relative connectedness of graphs; Poincaré-type inequality; Cayley graph of groups

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