Green's functions, electric networks, and the geometry of hyperbolic Riemann surfaces
Diller, Jeffrey
Illinois J. Math., Tome 45 (2001) no. 4, p. 453-485 / Harvested from Project Euclid
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We compare Green's function $g$ on an infinite volume, hyperbolic Riemann surface $X$ with an analogous discrete function $g_{\disc}$ on a graphical caricature $\Gamma$ of $X$. The main result, modulo technical hypotheses, is that $g$ and $g_{\disc}$ differ by at most an additive constant $C$ which depends only on the Euler characteristic of $X$. In particular, the estimate of $g$ by $g_{\disc}$ remains uniform as the geometry (i.e., the conformal structure) of $X$ varies.
Publié le : 2001-04-15
Classification:  30F15,  30F45,  31C20 
@article{1258138350,
     author = {Diller, Jeffrey},
     title = {Green's functions, electric networks, and the geometry of hyperbolic Riemann surfaces},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 453-485},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138350}
}

Diller, Jeffrey. Green's functions, electric networks, and the geometry of hyperbolic Riemann surfaces. Illinois J. Math., Tome 45 (2001) no. 4, pp.  453-485. http://gdmltest.u-ga.fr/item/1258138350/