We investigate connections between potential theories on a Ahlfors-regular metric space $X$, on a graph $G$ associated with $X$, and on the tree $T$ obtained by removing the ``horizontal edges'' in $G$. Applications to the calculation of set capacity are given.
N. Arcozzi, R. Rochberg, E. Sawyer, B. Wick. (2014). Potential Theory on Trees, Graphs and Ahlfors Regular Metric Spaces. POTENTIAL ANALYSIS, 41(2), 317-366 [10.1007/s11118-013-9371-8].
Potential Theory on Trees, Graphs and Ahlfors Regular Metric Spaces
ARCOZZI, NICOLA;
2014
Abstract
We investigate connections between potential theories on a Ahlfors-regular metric space $X$, on a graph $G$ associated with $X$, and on the tree $T$ obtained by removing the ``horizontal edges'' in $G$. Applications to the calculation of set capacity are given.File in questo prodotto:
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