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arXiv · 1611.00987

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

Paul Gauthier·Vassili Nestoridis·Athanase Papadopoulos
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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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Paul Gauthier, Vassili Nestoridis, Athanase Papadopoulos. 2016-11-03. Spherical arc-length as a global conformal parameter for analytic curves in the Riemann sphere. https://arxiv.org/abs/1611.00987

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