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 the 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 Erdös [4], and leads to more further interesting investigations (see the end of the article).
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Acknowledgement
This work is partially supported by China’s Recruitement Program of Global Experts, the School of Mathematics and Systems Science, Beihang University, and the National Natural Science Foundation of China (Grant No. 11871090).
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Liang, X. On the dimension of the k-medial axis for an arbitrary closed set. JAMA 147, 29–39 (2022). https://doi.org/10.1007/s11854-022-0202-y
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DOI: https://doi.org/10.1007/s11854-022-0202-y