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<p>We show that the (multi)function of the closest points is locally Lipschitz outside of the medial axis of a closed set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X\subset \mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>. With this result, we prove that the medial axis of <i>X</i> approaches every point where <i>X</i> is not Lipschitz normally embedded.</p>

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Medial axis detects non-Lipschitz normally embedded points

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  • 发表日期：

    2026年2月7日

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摘要

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