Spherical Arc-length as a Global Conformal Parameter for Analytic Curves in the Riemann Sphere
نویسندگان
چکیده
We 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 R and C and we discuss the situation of curves in the Riemann sphere C ∪ {∞}. AMS Mathematics Subject Classification: 30B40, 32B15
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تاریخ انتشار 2016