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Algebra i Analiz, 2021, Volume 33, Issue 6, Pages 214–234 (Mi aa1793)  
This article is cited in 1 scientific paper (total in 1 paper)

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Geometry of planar curves intersecting many lines in a few points

D. Vardakisa, A. Volbergab

a Department of Mathematics, Michigan State University, East Lansing, MI. 48823
b Hausdorff Center for Mathematics, Bonn, Germany
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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.
Keywords: Hausdorff dimension, Lipschitz function, Marstrand's theorem.
Received: 15.03.2021
English version:
St. Petersburg Mathematical Journal, 2022, Volume 33, Issue 6, Pages 1047–1062
DOI: https://doi.org/10.1090/spmj/1742
Document Type: Article
Language: English
Citation: D. Vardakis, A. Volberg, “Geometry of planar curves intersecting many lines in a few points”, Algebra i Analiz, 33:6 (2021), 214–234; St. Petersburg Math. J., 33:6 (2022), 1047–1062
Citation in format AMSBIB
\Bibitem{VarVol21}
\by D.~Vardakis, A.~Volberg
\paper Geometry of planar curves intersecting many lines in a few points
\jour Algebra i Analiz
\yr 2021
\vol 33
\issue 6
\pages 214--234
\mathnet{http://mi.mathnet.ru/aa1793}
\transl
\jour St. Petersburg Math. J.
\yr 2022
\vol 33
\issue 6
\pages 1047--1062
\crossref{https://doi.org/10.1090/spmj/1742}
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    • This publication is cited in the following 1 articles:
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