Arc length as a conformal parameter for locally analytic curves
Complex Variables
2015-09-01 v1 Metric Geometry
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 (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.
Cite
@article{arxiv.1508.07694,
title = {Arc length as a conformal parameter for locally analytic curves},
author = {Vassili Nestoridis and Athanase Papadopoulos},
journal= {arXiv preprint arXiv:1508.07694},
year = {2015}
}