Open Access
September 2004 Random Construction of Riemann Surfaces
Robert Brooks, Eran Makover
J. Differential Geom. 68(1): 121-157 (September 2004). DOI: 10.4310/jdg/1102536712


We develop a new approach for the study of “typical” Riemann surfaces with high genus. The method that we use is the construction of random Riemann surfaces from oriented cubic graphs. This construction enables us to get a control over the global geometry properties of compact Riemann surfaces. We use the theory of random regular graphs to show that almost all such surfaces have large first eigenvalues and large Cheeger constants. Moreover a closer analysis of the probability space of oriented cubic graphs shows that on a typical surface there is a large embedded hyperbolic ball.


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Robert Brooks. Eran Makover. "Random Construction of Riemann Surfaces." J. Differential Geom. 68 (1) 121 - 157, September 2004.


Published: September 2004
First available in Project Euclid: 8 December 2004

zbMATH: 1095.30037
MathSciNet: MR2152911
Digital Object Identifier: 10.4310/jdg/1102536712

Rights: Copyright © 2004 Lehigh University

Vol.68 • No. 1 • September 2004
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