Arc length as a conformal parameter for locally analytic curves

Vassili Nestoridis (1) , Athanase Papadopoulos (2)

1 Department of Mathematics [Athens]
2 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: Analytic curve; locally analytic curve; conformal parameter; arc length; analytic extension

Domaines: Variables complexes [math.CV]; Géométrie métrique [math.MG]

Vassili Nestoridis, Athanase Papadopoulos. Arc length as a conformal parameter for locally analytic curves. 2015. ⟨hal-01188475⟩