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

2016/11/03 by Gauthier, Paul, Nestoridis, Vassili, Papadopoulos, Athanase
#Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1611.00987

Abstract

We prove that for every analytic curve in the complex plane, Euclidean and spherical arc-lengths are global conformal 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 Euclidean n-space and complex n-space and we discuss the situation of curves in the Riemann sphere.

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