Geodesic
Geometry of planar curves intersecting many lines in a few points
Algebra i analiz, Tome 33 (2021) no. 6, pp. 214-234.

Voir la notice de l'article provenant de la source Math-Net.Ru

The local Lipschitz property is shown for the graph avoiding multiple point intersection with lines directed in a given cone. The assumption is much stronger than those of Marstrand's well-known theorem, but the conclusion is much stronger too. Additionally, a continuous curve with a similar property is $\sigma$-finite with respect to Hausdorff length and an estimate on the Hausdorff measure of each “piece” is found.
Keywords: Hausdorff dimension, Lipschitz function, Marstrand's theorem. 
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D. Vardakis; A. Volberg. Geometry of planar curves intersecting many lines in a few points. Algebra i analiz, Tome 33 (2021) no. 6, pp. 214-234. http://geodesic.mathdoc.fr/item/AA_2021_33_6_a10/

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