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arXiv · 2107.09634

Quantitative straightening of distance spheres

Guy C. David·McKenna Kaczanowski·Dallas Pinkerton
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Abstract

We study "distance spheres": the set of points lying at constant distance from a fixed arbitrary subset $K$ of $[0,1]^d$. We show that, away from the regions where $K$ is "too dense" and a set of small volume, we can decompose $[0,1]^d$ into a finite number of sets on which the distance spheres can be "straightened" into subsets of parallel $(d-1)$-dimensional planes by a bi-Lipschitz map. Importantly, the number of sets and the bi-Lipschitz constants are independent of the set $K$.

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Guy C. David, McKenna Kaczanowski, Dallas Pinkerton. 2021-07-20. Quantitative straightening of distance spheres. https://arxiv.org/abs/2107.09634

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