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- ItemSpherical arc-length as a global conformal parameter for analytic curves in the Riemann sphere(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Gauthier, Paul; Nestoridis, Vassili; Papadopoulos, AthanaseWe prove that for every analytic curve in the complex plane C, 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 Rn and Cn and we discuss the situation of curves in the Riemann sphere C {∞}.