On the piecewise approximation of bi-Lipschitz curves

  • Aldo Pratelli

    Universität Erlangen-Nürnberg, Germany
  • Emanuela Radici

    Universität Erlangen-Nürnberg, Germany


In this paper we deal with the task of uniformly approximating an LL-bi-Lipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are LL'-bi-Lipschitz, for instance this was already done with L=4LL'=4L in [3, Lemma 5.5]. The main result of this paper is to do the same with L=L+ϵL'=L+\epsilon (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. 1–37

DOI 10.4171/RSMUP/138-1