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arXiv · 1909.03203

Geometry of planar curves intersecting many lines in a few points

Dimitris Vardakis·Alexander Volberg
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Abstract

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.

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Dimitris Vardakis, Alexander Volberg. 2019-09-07. Geometry of planar curves intersecting many lines in a few points. https://arxiv.org/abs/1909.03203

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