Revista Matemática Iberoamericana

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Volume 26, Issue 2, 2010, pp. 367–448
DOI: 10.4171/RMI/605

Published online: 2010-08-31

Convergence of metric graphs and energy forms

Atsushi Kasue[1]

(1) Kanazawa University, Japan

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.

Keywords: Network, resistance form, resistance metric, Gromov-Hausdorff convergence, Γ-convergence, harmonic function of finite Dirichlet sum, Kuramochi compactification

Kasue Atsushi: Convergence of metric graphs and energy forms. Rev. Mat. Iberoamericana 26 (2010), 367-448. doi: 10.4171/RMI/605