Maximal sections of the unit ball of $l^n_p(\mathbb{C})$ for $p > 2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909536888029184 |
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| author | Jakimiuk, Jacek König, Hermann |
| author_facet | Jakimiuk, Jacek König, Hermann |
| contents | Eskenazis, Nayar and Tkocz have shown recently some resilience of Ball's celebrated cube slicing theorem, namely its analogue in $l^n_p$ for large $p$. We show that the complex analogue, i.e. resilience of the polydisc slicing theorem proven by Oleszkiewicz and Pelczyński, holds for large $p$ and small $n$, but does not hold for any $p > 2$ and large $n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_12552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal sections of the unit ball of $l^n_p(\mathbb{C})$ for $p > 2$ Jakimiuk, Jacek König, Hermann Functional Analysis Metric Geometry Probability 52A38, 52A40 (Primary), 46 B07, 60F05 (Secondary) Eskenazis, Nayar and Tkocz have shown recently some resilience of Ball's celebrated cube slicing theorem, namely its analogue in $l^n_p$ for large $p$. We show that the complex analogue, i.e. resilience of the polydisc slicing theorem proven by Oleszkiewicz and Pelczyński, holds for large $p$ and small $n$, but does not hold for any $p > 2$ and large $n$. |
| title | Maximal sections of the unit ball of $l^n_p(\mathbb{C})$ for $p > 2$ |
| topic | Functional Analysis Metric Geometry Probability 52A38, 52A40 (Primary), 46 B07, 60F05 (Secondary) |
| url | https://arxiv.org/abs/2402.12552 |