Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

PETRA BONFERT–TAYLORa1, MARTIN BRIDGEMANa2, RICHARD D. CANARYa3§ and EDWARD C. TAYLORa4

a1 Wesleyan University, Middletown, CT 06459, U.S.A. e-mail: pbonfert@wesleyan.edu

a2 Boston College, Chestnut Hill, MA 02467, U.S.A. e-mail: bridgem@bc.edu

a3 University of Michigan, Ann Arbor, MI 48109, U.S.A. e-mail: canary@umich.edu

a4 Wesleyan University, Middletown, CT 06459, U.S.A. e-mail: ectaylor@wesleyan.edu

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.

(Received December 22 2005)

(Revised October 02 2006)

Footnotes

† Supported in part by NSF grant 0305704.

‡ Supported in part by NSF grant 0305634.

§ Supported in part by NSF grants 0203698 and 0504791.