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Uniformisation of the twice–punctured disc - problems of confluence

Published online by Cambridge University Press:  17 April 2009

Joachim A. Hempel  and
Simon J. Smith
Joachim A. Hempel
Affiliation:
Department of Mathematics Statistics and Computing Science, University of New England, Armidale, N.S.W., 2351, Australia
Simon J. Smith
Affiliation:
Department of Mathematics, Bendigo College of Advanced Education, P.O. Box 199, Bendigo, Victoria, 3550, Australia
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Abstract

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For the twice-punctured unit disc Ωp = {z: |z| < 1, z ≠ ±p}, where 0 < p < 1, we obtain precise descriptions for p near 0 of various parameters associated with the uniformisation of Ωp by the upper half-plane U = {τ: Im τ > 0}. These parameters include the hyperbolic length of the geodesic surrounding ±p, the so-called “accessory parameters”, and the “proximity parameter” which determines the behaviour of the hyperbolic density near the punctures of Ωp.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 369 - 387
Copyright
Copyright © Australian Mathematical Society 1989

References

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