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Kasue, Atsushi

Convergence of metric graphs and energy forms. (English) Zbl 1196.31004

Rev. Mat. Iberoam. 26, No. 2, 367-448 (2010).
Summary: 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 the 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.

Cited in 15 Documents

MSC:

31C20 Discrete potential theory
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

network; resistance form; resistance metric; Gromov-Hausdorff convergence; \(\Gamma\)-convergence; Kuramochi compactification
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\textit{A. Kasue}, Rev. Mat. Iberoam. 26, No. 2, 367--448 (2010; Zbl 1196.31004)
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References:

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