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The construction of branched covering Riemann surfaces

Published online by Cambridge University Press:  18 May 2009

R. A. Rankin
R. A. Rankin
Affiliation:
The University Glasgow
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In some recent work on uniformization [2], I found it necessary to consider a regular branched covering Riemann surface Ȓ of a given Riemann surface Rf, where Rf is an unlimited branched, but not necessarily regular, covering surface of a portion Rz of the extended complex z-plane Z(2-sphere). The branching of Ȓ over Rf had to be chosen so that Ȓ was regular over Rz, since the uniformization of the functions on Rf is then simpler; in particular, the Schwarzian derivative is then a single-valued function of z.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 4 , July 1958 , pp. 199 - 207
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

REFERENCES

1.Fourés, L., Sur les recouvrements regulièrement ramifiés, Bull. Sci. Math. 76 (1962), 17–32.Google Scholar
2.Rankin, R. A., The Schwarzian derivative and uniformization, Journal d'Analyse. 6 (1958).Google Scholar
3.Springer, G., Introduction to Riemann surfaces (Reading, 1957).Google Scholar