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arXiv · 1908.06000

On the union of essentially distinct $\delta$-tubes

Qiuyu Ren
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Abstract

We say two $\delta$-tubes (dimension $\delta\times\cdots\times\delta\times1$) in $\mathbb{R}^n$ are essentially distinct if the measure of their intersection is smaller than a half of a single $\delta$-tube. For a collection of essentially distinct $\delta$-tubes, we give the asymptotically sharp lower bound for the measure of their union. Then we characterize all sharp examples. We will give a new measurement of convexity based on the X-ray transform.

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Qiuyu Ren. 2019-08-16. On the union of essentially distinct $\delta$-tubes. https://arxiv.org/abs/1908.06000

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