Teichmüller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces
نویسندگان
چکیده
We show that there exists a universal constant Kc so that every K-strongly quasiconformally homogeneous hyperbolic surface X (not equal to H2) has the property that K > Kc > 1. The constant Kc is the best possible, and is computed in terms of the diameter of the (2, 3, 7)-hyperbolic orbifold (which is the hyperbolic orbifold of smallest area.) We further show that the minimum strong homogeneity constant of a hyperbolic surface without conformal automorphisms decreases if one passes to a non-amenable regular cover.
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