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

@article{RSMUP_2017__138__1_0,
     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},
     year = {2017},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {138},
     doi = {10.4171/RSMUP/138-1},
     mrnumber = {3743243},
     zbl = {1391.46041},
     url = {https://www.numdam.org/articles/10.4171/RSMUP/138-1/}
}

TY  - JOUR
AU  - Pratelli, Aldo
AU  - Radici, Emanuela
TI  - On the piecewise approximation of bi-Lipschitz curves
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2017
SP  - 1
EP  - 37
VL  - 138
PB  - European Mathematical Society Publishing House
PP  - Zuerich, Switzerland
UR  - https://www.numdam.org/articles/10.4171/RSMUP/138-1/
DO  - 10.4171/RSMUP/138-1
ID  - RSMUP_2017__138__1_0
ER  -

%0 Journal Article
%A Pratelli, Aldo
%A Radici, Emanuela
%T On the piecewise approximation of bi-Lipschitz curves
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2017
%P 1-37
%V 138
%I European Mathematical Society Publishing House
%C Zuerich, Switzerland
%U https://www.numdam.org/articles/10.4171/RSMUP/138-1/
%R 10.4171/RSMUP/138-1
%F RSMUP_2017__138__1_0

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

Cité par Sources :