Arc length as a conformal parameter for locally analytic curves

2015/08/31 by Vassili Nestoridis, Athanase Papadopoulos, Nestoridis, Vassili +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG) #math.CV #math.MG

paper · pdf · doi:10.48550/arxiv.1508.07694

arxiv created 2015/08/31 · arxiv updated 2015/09/01

Abstract

For any locally analytic curve we show that arc length can be complexified and seen as a conformal parameter. As an application, we show that any such curve defines a unique maximal one and that the notions of analytic Jordan curve coincides with the notion of a Jordan curve which is locally analytic. We give examples where we also find, for a curve γ(s), the limit sets of the largest extensions, that is, the limit set of the curve as s converges to the end point of the interval.

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