The construction of branched covering Riemann surfaces
Glasgow mathematical journal, Tome 2 (1958) no. 4, pp. 199-207
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Rankin, R. A. The construction of branched covering Riemann surfaces. Glasgow mathematical journal, Tome 2 (1958) no. 4, pp. 199-207. doi: 10.1017/S2040618500033724
@article{10_1017_S2040618500033724,
author = {Rankin, R. A.},
title = {The construction of branched covering {Riemann} surfaces},
journal = {Glasgow mathematical journal},
pages = {199--207},
year = {1958},
volume = {2},
number = {4},
doi = {10.1017/S2040618500033724},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033724/}
}
[1] 1.Fourés, L., Sur les recouvrements regulièrement ramifiés, Bull. Sci. Math. 76 (1962), 17–32. Google Scholar
[2] 2.Rankin, R. A., The Schwarzian derivative and uniformization, Journal d'Analyse. 6 (1958). Google Scholar
[3] 3.Springer, G., Introduction to Riemann surfaces (Reading, 1957). Google Scholar
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