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Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

  • PETRA BONFERT–TAYLOR (a1), MARTIN BRIDGEMAN (a2), RICHARD D. CANARY (a3) and EDWARD C. TAYLOR (a4)
Abstract
Abstract

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.

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[13] A. Yamada . On Marden's universal constant of Fuchsian groups. Kodai Math. J. 4 (1981), 266277.

[14] A. Yamada . On Marden's universal constant of Fuchsian groups II. J. Analyse Math. 41 (1982), 234248.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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