When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular
Differential Geometry
2026-04-30 v1
Abstract
We prove a necessary and sufficient condition for a -hypersurface to have all parallel sets nowhere -regular. As a corollary, we deduce that for a generic -regular convex body all interior parallel bodies have nowhere -regular boundaries.
Cite
@article{arxiv.2604.26764,
title = {When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular},
author = {Mario Santilli},
journal= {arXiv preprint arXiv:2604.26764},
year = {2026}
}