Potential Theory on Trees, Graphs and Ahlfors-regular Metric Spaces

Nicola Arcozzi; Richard Rochberg; Eric T. Sawyer; Brett D. Wick

doi:10.1007/s11118-013-9371-8

Potential Theory on Trees, Graphs and Ahlfors-regular Metric Spaces

Nicola Arcozzi
, Richard Rochberg
, Eric T. Sawyer
, Brett D. Wick

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Pages (from-to)	317-366
Number of pages	50
Journal	Potential Analysis
Volume	41
Issue number	2
DOIs	https://doi.org/10.1007/s11118-013-9371-8
State	Published - Jun 2014

Keywords

Ahlfors-regular metric space
Capacity
Potential theory

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10.1007/s11118-013-9371-8

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title = "Potential Theory on Trees, Graphs and Ahlfors-regular Metric Spaces",

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.",

keywords = "Ahlfors-regular metric space, Capacity, Potential theory",

author = "Nicola Arcozzi and Richard Rochberg and Sawyer, \{Eric T.\} and Wick, \{Brett D.\}",

year = "2014",

month = jun,

doi = "10.1007/s11118-013-9371-8",

language = "English",

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journal = "Potential Analysis",

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T1 - Potential Theory on Trees, Graphs and Ahlfors-regular Metric Spaces

AU - Arcozzi, Nicola

AU - Rochberg, Richard

AU - Sawyer, Eric T.

AU - Wick, Brett D.

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

KW - Ahlfors-regular metric space

KW - Capacity

KW - Potential theory

UR - https://www.scopus.com/pages/publications/84904515973

U2 - 10.1007/s11118-013-9371-8

DO - 10.1007/s11118-013-9371-8

M3 - Article

AN - SCOPUS:84904515973

SN - 0926-2601

VL - 41

SP - 317

EP - 366

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

Potential Theory on Trees, Graphs and Ahlfors-regular Metric Spaces

Abstract

Keywords

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