On the piecewise approximation of bi-Lipschitz curves
Pratelli, Aldo1 ; Radici, Emanuela1
1 Universität Erlangen-Nürnberg, Germany
Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 1-37.

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 ' =4L 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 :
DOI : 10.4171/RSMUP/138-1
Classification : 46
Mots clés : Approximation of curves, bi-Lipschitz curves
Pratelli, Aldo 1 ; Radici, Emanuela 1

1 Universität Erlangen-Nürnberg, Germany 
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     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},
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     volume = {138},
     year = {2017},
     doi = {10.4171/RSMUP/138-1},
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     zbl = {1391.46041},
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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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