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February 9, 2026Archiv der Mathematik0 citationsOpen Access

Medial axis detects non-Lipschitz normally embedded points

ABAdam Białożyt

Key Points

  • The aim is to explore the local Lipschitz properties of the closest points function outside the medial axis of a closed set.
  • Analyzed the properties of the closest points function
  • Examined local Lipschitz conditions
  • Investigated medial axis behavior concerning Lipschitz normal embeddings
  • Identified closest points function as being locally Lipschitz outside medial axis
  • Established that medial axis reaches non-Lipschitz normally embedded points

Abstract

Abstract We show that the (multi) function of the closest points is locally Lipschitz outside of the medial axis of a closed set X Rⁿ X ⊂ R n. With this result, we prove that the medial axis of X approaches every point where X is not Lipschitz normally embedded.

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Cite This Study

Adam Białożyt (2026) studied this question.

synapsesocial.com/papers/69897a86f0ec2af6756e8bd6https://doi.org/10.1007/s00013-025-02216-9
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