In this paper we deal with the task of uniformly approximating an -bi-Lipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are -bi-Lipschitz, for instance this was already done with in [3, 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.
Cite this article
Aldo Pratelli, Emanuela Radici, On the piecewise approximation of bi-Lipschitz curves. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 1–37DOI 10.4171/RSMUP/138-1