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September, 2002 On The Asymptotic Isoperimetric Constants for Riemann Surfaces and Graphs
Robert Brooks, Andrzej Zuk
J. Differential Geom. 62(1): 49-78 (September, 2002). DOI: 10.4310/jdg/1090425529


We study the behavior of the Cheeger isoperimetric constant on infinite families of graphs and Riemann surfaces, and its relationship to the first eigenvalue λ1 of the Laplacian. We adapt probabilistic arguments of Bollobás to the setting of Riemann surfaces, and then show that Cheeger constants of the modular surfaces are uniformly bounded from above away from the maximum value. We extend this result to the class of Ramanujan surfaces, defined below.


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Robert Brooks. Andrzej Zuk. "On The Asymptotic Isoperimetric Constants for Riemann Surfaces and Graphs." J. Differential Geom. 62 (1) 49 - 78, September, 2002.


Published: September, 2002
First available in Project Euclid: 21 July 2004

zbMATH: 1065.05091
MathSciNet: MR1987377
Digital Object Identifier: 10.4310/jdg/1090425529

Rights: Copyright © 2002 Lehigh University

Vol.62 • No. 1 • September, 2002
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