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.
Publié le : 2010-06-15
Classification:
network,
resistance form,
resistance metric,
Gromov-Hausdorff convergence,
$\Gamma$-convergence,
harmonic function of finite Dirichlet sum,
Kuramochi compactification,
31C20,
53C23,
60J10
@article{1275671307,
author = {Kasue
,
Atsushi},
title = {Convergence of metric graphs and energy forms},
journal = {Rev. Mat. Iberoamericana},
volume = {26},
number = {1},
year = {2010},
pages = { 367-448},
language = {en},
url = {http://dml.mathdoc.fr/item/1275671307}
}
Kasue
,
Atsushi. Convergence of metric graphs and energy forms. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp. 367-448. http://gdmltest.u-ga.fr/item/1275671307/