JournalsrmiVol. 26, No. 2pp. 367–448

Convergence of metric graphs and energy forms

  • Atsushi Kasue

    Kanazawa University, Japan
Convergence of metric graphs and energy forms cover
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Abstract

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 Γ\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.

Cite this article

Atsushi Kasue, Convergence of metric graphs and energy forms. Rev. Mat. Iberoam. 26 (2010), no. 2, pp. 367–448

DOI 10.4171/RMI/605