Spherical arc-length as a global holomorphic parameter for analytic curves in the Riemann sphere

We prove that for every analytic curve in the complex plane C, Euclidean and spherical arc-lengths are global holomorphic parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case o...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-11, Vol.455 (1), p.742-749
Main Authors: Gauthier, Paul M., Nestoridis, Vassili, Papadopoulos, Athanase
Format: Article
Language:English
Subjects:
Analytic curve
Analytic extension
Arc-length
Geometric Topology
Global parameter
Mathematics
Maximal extension
Spherical arc-length
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Summary:We prove that for every analytic curve in the complex plane C, Euclidean and spherical arc-lengths are global holomorphic parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in Rn and Cn and we discuss the situation of curves in the Riemann sphere C∪{∞}.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.06.003