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arXiv · 2404.13540

On the dimension of k-medial axis for arbitrary closed set

Xiangyu Liang
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Abstract

We prove that the k-medial axis of an arbitrary closed set in Rn is n-k+1-rectifiable (and hence of dimension at most n-k+1). This result gives a first stratification for medial axis of any closed set, which has been widely studied and used in pure and applied mathematics. This also answers a question proposed by Erdos[4], and leads to more further interesting investigations (see the end of the article).

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Xiangyu Liang. 2024-04-21. On the dimension of k-medial axis for arbitrary closed set. https://arxiv.org/abs/2404.13540

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