Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

• Autores: Petra Bonfert Taylor, Martin Bridgeman, Richard D. Canary, Edward C. Taylor
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 1, 2007, págs. 71-84
• Idioma: inglés
• DOI: 10.1017/s0305004107000138
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• Resumen

  • We show that any closed hyperbolic surface admitting a conformal automorphism with ¿many¿ fixed points is uniformly quasiconformally homogeneous, with constant uniformly bounded away from 1. In particular, there is a uniform lower bound on the quasiconformal homogeneity constant for all hyperelliptic surfaces. In addition, we introduce more restrictive notions of quasiconformal homogeneity and bound the associated quasiconformal homogeneity constants uniformly away from 1 for all hyperbolic surfaces.