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Potential Theory on Trees,Graphs and Ahlfors-regular Metric Spaces |
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| Authors: | Nicola Arcozzi Richard Rochberg Eric T. Sawyer Brett D. Wick |
| Affiliation: | 1. Dipartimento di Matematica, Universita di Bologna, 40127, Bologna, Italy 2. Department of Mathematics, Washington University, St. Louis, MO, 63130, USA 3. Department of Mathematics & Statistics, McMaster University, Hamilton, ON, Canada, L8S 4K1 4. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332–0160, USA |
| 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. |
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