On Sections of Convex Bodies in John's Position and of Generalised $B_p^n$ Balls
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915897788071936 |
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| author | Alonso-Gutiérrez, David Brazitikos, Silouanos Chasapis, Giorgos |
| author_facet | Alonso-Gutiérrez, David Brazitikos, Silouanos Chasapis, Giorgos |
| contents | We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp-Lieb inequality with a generalised Parseval-type identity. This lets us complement some earlier results of the first two named authors, as well as generalise the classical estimates of Meyer-Pajor and Koldobsky regarding extremal sections of $B_p^n$ balls to a broader family of norms induced by a John's decomposition of the identity in $\mathbb{R}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14047 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Sections of Convex Bodies in John's Position and of Generalised $B_p^n$ Balls Alonso-Gutiérrez, David Brazitikos, Silouanos Chasapis, Giorgos Metric Geometry Functional Analysis Primary 52A23, Secondary 60D05 We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp-Lieb inequality with a generalised Parseval-type identity. This lets us complement some earlier results of the first two named authors, as well as generalise the classical estimates of Meyer-Pajor and Koldobsky regarding extremal sections of $B_p^n$ balls to a broader family of norms induced by a John's decomposition of the identity in $\mathbb{R}^n$. |
| title | On Sections of Convex Bodies in John's Position and of Generalised $B_p^n$ Balls |
| topic | Metric Geometry Functional Analysis Primary 52A23, Secondary 60D05 |
| url | https://arxiv.org/abs/2510.14047 |