Open Access
June, 2010 Convergence of metric graphs and energy forms
Atsushi Kasue
Rev. Mat. Iberoamericana 26(2): 367-448 (June, 2010).


In this paper, we begin with clarifying spaces obtained as limits of sequences of finite networks from an analytic point of view, and we discuss convergence of finite networks with respect to the topology of both the Gromov-Hausdorff distance and variational convergence called $\Gamma$-convergence. Relevantly to convergence of finite networks to infinite ones, we investigate the space of harmonic functions of finite Dirichlet sums on infinite networks and their Kuramochi compactifications.


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Atsushi Kasue . "Convergence of metric graphs and energy forms." Rev. Mat. Iberoamericana 26 (2) 367 - 448, June, 2010.


Published: June, 2010
First available in Project Euclid: 4 June 2010

zbMATH: 1196.31004
MathSciNet: MR2677003

Primary: 31C20
Secondary: 53C23 , 60J10

Keywords: $\Gamma$-convergence , Gromov-Hausdorff convergence , harmonic function of finite Dirichlet sum , Kuramochi compactification , network , Resistance form , resistance metric

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.26 • No. 2 • June, 2010
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