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Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms

Published online by Cambridge University Press:  01 July 2007

PETRA BONFERT–TAYLOR ,
MARTIN BRIDGEMAN ,
RICHARD D. CANARY  and
EDWARD C. TAYLOR
PETRA BONFERT–TAYLOR
Affiliation:
Wesleyan University, Middletown, CT 06459, U.S.A. e-mail: [email protected]
MARTIN BRIDGEMAN
Affiliation:
Boston College, Chestnut Hill, MA 02467, U.S.A. e-mail: [email protected]
RICHARD D. CANARY
Affiliation:
University of Michigan, Ann Arbor, MI 48109, U.S.A. e-mail: [email protected]
EDWARD C. TAYLOR
Affiliation:
Wesleyan University, Middletown, CT 06459, U.S.A. e-mail: [email protected]
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 71 - 84
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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