Ball-convex bodies and $L_p$ relative surface areas
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914215235682304 |
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| author | Werner, Elisabeth M. Yalikun, Diliya |
| author_facet | Werner, Elisabeth M. Yalikun, Diliya |
| contents | We define new surface area measures for ball-convex bodies which we call $L_p$ relative surface areas. We show that those are rigid motion invariant valuations. We establish inequalities for these quantities and prove a monotonicity behavior which leads to a new notion of entropy for ball-convex bodies. We introduce a weighted ball floating body. A derivative of volume of a ball-convex body with a weighted ball floating body provides a geometric interpretation of the $L_p$ relative surface areas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ball-convex bodies and $L_p$ relative surface areas Werner, Elisabeth M. Yalikun, Diliya Metric Geometry Differential Geometry We define new surface area measures for ball-convex bodies which we call $L_p$ relative surface areas. We show that those are rigid motion invariant valuations. We establish inequalities for these quantities and prove a monotonicity behavior which leads to a new notion of entropy for ball-convex bodies. We introduce a weighted ball floating body. A derivative of volume of a ball-convex body with a weighted ball floating body provides a geometric interpretation of the $L_p$ relative surface areas. |
| title | Ball-convex bodies and $L_p$ relative surface areas |
| topic | Metric Geometry Differential Geometry |
| url | https://arxiv.org/abs/2512.19836 |