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On the dimension of k-medial axis for arbitrary closed set
Published 21 Apr 2024 in math.CA | (2404.13540v1)
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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