On the piecewise approximation of bi-Lipschitz curves
Classical Analysis and ODEs
2015-05-26 v1
Abstract
In this paper we deal with the task of uniformly approximating an -biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are -biLipschitz, for instance this was already done with in [Daneri-Pratelli, Lemma 5.5]. The main result of this paper is to do the same with (which is of course the best possible result); in the end, we generalize the result to the case of closed curves.
Keywords
Cite
@article{arxiv.1505.06510,
title = {On the piecewise approximation of bi-Lipschitz curves},
author = {Aldo Pratelli and Emanuela Radici},
journal= {arXiv preprint arXiv:1505.06510},
year = {2015}
}