Some inequalities of isoperimetric type for the c-affine surface area
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915452393881600 |
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| author | Artstein-Avidan, Shiri Chor, Arnon |
| author_facet | Artstein-Avidan, Shiri Chor, Arnon |
| contents | We study the c-affine surface area $Ω^c$, recently introduced by Schütt, Werner and Yalikun. We show that on the class of ball-bodies, $Ω^c$ is maximized by a ball of radius $\frac{n}{n+1}$, and that a Santaló-type inequality holds: $Ω^c(K) Ω^c(K^c) \leq Ω^c(\frac{1}{2} B_2^n)^2$. We also produce some more intricate inequalities involving the surface area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some inequalities of isoperimetric type for the c-affine surface area Artstein-Avidan, Shiri Chor, Arnon Metric Geometry 52A40 We study the c-affine surface area $Ω^c$, recently introduced by Schütt, Werner and Yalikun. We show that on the class of ball-bodies, $Ω^c$ is maximized by a ball of radius $\frac{n}{n+1}$, and that a Santaló-type inequality holds: $Ω^c(K) Ω^c(K^c) \leq Ω^c(\frac{1}{2} B_2^n)^2$. We also produce some more intricate inequalities involving the surface area. |
| title | Some inequalities of isoperimetric type for the c-affine surface area |
| topic | Metric Geometry 52A40 |
| url | https://arxiv.org/abs/2505.19172 |