On the dimension of k-medial axis for arbitrary closed set
Classical Analysis and ODEs
2024-04-23 v1
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).
Cite
@article{arxiv.2404.13540,
title = {On the dimension of k-medial axis for arbitrary closed set},
author = {Xiangyu Liang},
journal= {arXiv preprint arXiv:2404.13540},
year = {2024}
}
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8 pages