Area and antipodal distance in convex hypersurfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915949033029632 |
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| author | Dibble, James Hoisington, Joseph |
| author_facet | Dibble, James Hoisington, Joseph |
| contents | We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized lower bound for the volume of a Riemannian $n$-sphere, proved by Berger in dimension $n=2$ and disproved by Croke in dimensions $n \geq 3$, is valid for convex hypersurfaces in all dimensions. We also establish a sharp lower bound for the mean width of a convex hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Area and antipodal distance in convex hypersurfaces Dibble, James Hoisington, Joseph Differential Geometry Metric Geometry 52A38, 52A40, 53C23 (Primary) 52A39, 53C45, 53C65 (Secondary) We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized lower bound for the volume of a Riemannian $n$-sphere, proved by Berger in dimension $n=2$ and disproved by Croke in dimensions $n \geq 3$, is valid for convex hypersurfaces in all dimensions. We also establish a sharp lower bound for the mean width of a convex hypersurface. |
| title | Area and antipodal distance in convex hypersurfaces |
| topic | Differential Geometry Metric Geometry 52A38, 52A40, 53C23 (Primary) 52A39, 53C45, 53C65 (Secondary) |
| url | https://arxiv.org/abs/2604.02667 |