On the piecewise approximation of bi-Lipschitz curves

Pratelli, Aldo; Radici, Emanuela

doi:10.4171/RSMUP/138-1

Pratelli, Aldo ¹ ; Radici, Emanuela ¹

¹ Universität Erlangen-Nürnberg, Germany

Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 1-37.

Résumé

In this paper we deal with the task of uniformly approximating an $L$ -bi-Lipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are $L^{'}$ -bi-Lipschitz, for instance this was already done with $L^{'} = 4 L$ in [3, Lemma 5.5]. The main result of this paper is to do the same with $L^{'} = L + ϵ$ (which is of course the best possible result); in the end, we generalize the result to the case of closed curves.

Publié le : 2017-12-22

MR Zbl

DOI : 10.4171/RSMUP/138-1

Classification : 46
Mots-clés : Approximation of curves, bi-Lipschitz curves

Affiliations des auteurs :

Pratelli, Aldo ¹ ; Radici, Emanuela ¹

¹ Universität Erlangen-Nürnberg, Germany

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     author = {Pratelli, Aldo and Radici, Emanuela},
     title = {On the piecewise approximation of {bi-Lipschitz} curves},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--37},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {138},
     year = {2017},
     doi = {10.4171/RSMUP/138-1},
     mrnumber = {3743243},
     zbl = {1391.46041},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/138-1/}
}

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Pratelli, Aldo; Radici, Emanuela. On the piecewise approximation of bi-Lipschitz curves. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 1-37. doi : 10.4171/RSMUP/138-1. http://www.numdam.org/articles/10.4171/RSMUP/138-1/

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