Some comments on the mth-order Projection Bodies
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908748040110080 |
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| author | Langharst, Dylan |
| author_facet | Langharst, Dylan |
| contents | The celebrated Petty's projection inequality is a sharp upper bound for the volume of the polar projection body of a convex body. Lutwak introduced the concept of mixed projection bodies and extended Petty's projection inequality. Alonso-Gutiérrez later did a stability result for Petty's projection inequality.
In 1970, Schneider introduced the $m$th-order setting and extended the difference body to that setting. In a previous work, we, working with Haddad, Putterman, Roysdon, and Ye, established an extension of the projection body operator to this setting. In this note, we continue this study for the mixed projection body operator as well as the question of stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some comments on the mth-order Projection Bodies Langharst, Dylan Functional Analysis Metric Geometry 52A39, 52A40, Secondary: 28A75 The celebrated Petty's projection inequality is a sharp upper bound for the volume of the polar projection body of a convex body. Lutwak introduced the concept of mixed projection bodies and extended Petty's projection inequality. Alonso-Gutiérrez later did a stability result for Petty's projection inequality. In 1970, Schneider introduced the $m$th-order setting and extended the difference body to that setting. In a previous work, we, working with Haddad, Putterman, Roysdon, and Ye, established an extension of the projection body operator to this setting. In this note, we continue this study for the mixed projection body operator as well as the question of stability. |
| title | Some comments on the mth-order Projection Bodies |
| topic | Functional Analysis Metric Geometry 52A39, 52A40, Secondary: 28A75 |
| url | https://arxiv.org/abs/2504.18933 |