An extremal property of the symmetric decreasing rearrangement
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911459616751616 |
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| author | Hoehner, Steven Novaes, Júlia |
| author_facet | Hoehner, Steven Novaes, Júlia |
| contents | It is shown that for a given log-concave function, its symmetric decreasing rearrangement is always harder to approximate in the symmetric difference metric by inner log-linearizations with a fixed number of break points. This extends a classical result of Macbeath (1951) from convex bodies to a functional setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An extremal property of the symmetric decreasing rearrangement Hoehner, Steven Novaes, Júlia Functional Analysis Metric Geometry 39B62 (Primary) 52A20, 52A40, 52A41 (Secondary) It is shown that for a given log-concave function, its symmetric decreasing rearrangement is always harder to approximate in the symmetric difference metric by inner log-linearizations with a fixed number of break points. This extends a classical result of Macbeath (1951) from convex bodies to a functional setting. |
| title | An extremal property of the symmetric decreasing rearrangement |
| topic | Functional Analysis Metric Geometry 39B62 (Primary) 52A20, 52A40, 52A41 (Secondary) |
| url | https://arxiv.org/abs/2305.10501 |