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.
On the piecewise approximation of bi-lipschitz curves
Pratelli, Aldo;
2017-01-01
Abstract
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.File in questo prodotto:
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