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arXiv · 2604.26764

When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular

Mario Santilli
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Abstract

We prove a necessary and sufficient condition for a $ C^1 $-hypersurface to have all parallel sets nowhere $ C^1 $-regular. As a corollary, we deduce that for a generic $ C^1 $-regular convex body all interior parallel bodies have nowhere $ C^1 $-regular boundaries.

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Mario Santilli. 2026-04-29. When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular. https://arxiv.org/abs/2604.26764

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