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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Greenfield, Mark 2015. A lower bound for Torelli- $$K$$ K -quasiconformal homogeneity. Geometriae Dedicata, Vol. 177, Issue. 1, p. 61.

    Bonfert-Taylor, Petra Canary, Richard and Taylor, Edward C. 2014. Quasiconformal Homogeneity after Gehring and Palka. Computational Methods and Function Theory, Vol. 14, Issue. 2-3, p. 417.

    Vuorinen, M. and Zhang, X. 2014. Distortion of quasiconformal mappings with identity boundary values. Journal of the London Mathematical Society, Vol. 90, Issue. 3, p. 637.

    Kwakkel, Ferry and Markovic, Vladimir 2011. Quasiconformal homogeneity of genus zero surfaces. Journal d'Analyse Mathématique, Vol. 113, Issue. 1, p. 173.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 143, Issue 1
  • July 2007, pp. 71-84

Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

  • DOI:
  • Published online: 01 July 2007

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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[2]P. Bonfert-Taylor , R. D. Canary , G. Martin and E. C. Taylor . Quasiconformal homogeneity of hyperbolic manifolds. Math. Ann. 331 (2005), 281295.

[3]P. Bonfert-Taylor and E. C. Taylor . Hausdorff dimension and limit sets of quasiconformal groups. Mich. Math. J. 49 (2001), 243257.

[6]F. W. Gehring and B. Palka . Quasiconformally homogeneous domains. J. Analyse Math. 30 (1976), 172199.

[9]P. MacManus , R. Näkki and B. Palka . Quasiconformally bi-homogeneous compacta in the complex plane. Proc. London Math. Soc. 78 (1999), 215240.

[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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