When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914516939309056 |
|---|---|
| author | Santilli, Mario |
| author_facet | Santilli, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular Santilli, Mario Differential Geometry 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. |
| title | When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.26764 |