English

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 LL-biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are LL'-biLipschitz, for instance this was already done with L=4LL'= 4L in [Daneri-Pratelli, Lemma 5.5]. The main result of this paper is to do the same with L=L+εL'=L+ \varepsilon (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}
}