A necessary and sufficient condition is proved for C¹-hypersurfaces whose parallel sets are all nowhere C¹-regular, implying the same for generic convex bodies.
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When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular
A necessary and sufficient condition is proved for C¹-hypersurfaces whose parallel sets are all nowhere C¹-regular, implying the same for generic convex bodies.