平面曲线与许多直线相交于几个点的几何学

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-10-31 DOI:10.1090/spmj/1742

D. Vardakis, A. Volberg

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引用次数: 0

摘要

给出了避免在给定圆锥上与直线相交的多点图的局部Lipschitz性质。这个假设比著名的马斯特兰德定理要强得多，但结论也要强得多。此外，具有类似性质的连续曲线对Hausdorff长度是σ \ σ -有限的，并且找到了每个“片段”的Hausdorff测度的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Geometry of planar curves intersecting many lines at a few points

The local Lipschitz property is shown for the graphs 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 σ \sigma -finite with respect to Hausdorff length and an estimate on the Hausdorff measure of each “piece” is found.

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.