Abstract
Riemann surfaces were introduced to build new domains of definition on which multivalued algebraic functions become univalued. One of the advantages of algebraic functions which was lost in this procedure was the ability to use a single parameter in order to describe the function in its full domain of definition (which becomes the whole Riemann surface). In fact, this advantage is still available if one lifts the function to the universal covering of the Riemann surface, as shown by the following uniformization theorem
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References
H.P. de Saint-Gervais (pen name of the collective: A. Alvarez, C. Bavard, F. Béguin, N. Bergeron, M. Bourrigan, B. Deroin, S. Dumitrescu, C. Frances, É. Ghys, A. Guilloux, F. Loray, P. Popescu-Pampu, P. Py, B. Sévennec, J.-C. Sikorav), Uniformization of Riemann surfaces. Revisiting a hundred-year-old theorem. Eur. Math. Soc. (2016). Translated from the 2011 French edition by R.G. Burns
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Popescu-Pampu, P. (2016). The Uniformization of Riemann Surfaces. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_24
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DOI: https://doi.org/10.1007/978-3-319-42312-8_24
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42311-1
Online ISBN: 978-3-319-42312-8
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