Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 4
  • Cited by
    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

  • PETRA BONFERT–TAYLOR (a1), MARTIN BRIDGEMAN (a2), RICHARD D. CANARY (a3) and EDWARD C. TAYLOR (a4)
  • DOI: http://dx.doi.org/10.1017/S0305004107000138
  • Published online: 01 July 2007
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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×