On The Asymptotic Isoperimetric Constants for Riemann Surfaces and Graphs
On The Asymptotic Isoperimetric Constants for Riemann Surfaces and Graphs
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 …