Inserted: 8 may 2015
Last Updated: 28 oct 2022
Journal: Rend. Sem. Mat. Univ. Padova
In this paper we deal with the task of uniformly approximating an $L$-biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are $L'$-biLipschitz, for instance this was already done with $L'= 4L$ in Daneri-Pratelli, Lemma 5.5. The main result of this paper is to do the same with $L'=L+ \varepsilon$ (which is of course the best possible result); in the end, we generalize the result to the case of closed curves.