General Higher Order $L^p$ Mean Zonoids
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910980950196224 |
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| author | Langharst, Dylan Xi, Dongmeng |
| author_facet | Langharst, Dylan Xi, Dongmeng |
| contents | In 1970, Schneider introduced the higher-order difference body and the associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman, Roysdon and Ye expanded the concept to a burgeoning higher-order Brunn-Minkowski theory. In 1991, Zhang introduced mean zonoids of a convex body, which was extended to the Firey-Brunn-Minkowski theory setting by Xi, Guo and Leng in 2014. In this note, we extend these $L^p$ mean zonoids to the higher-order setting and establish the associated isoperimetric inequality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_09500 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | General Higher Order $L^p$ Mean Zonoids Langharst, Dylan Xi, Dongmeng Metric Geometry Functional Analysis 52A30, 52A40, Secondary: 28A75 In 1970, Schneider introduced the higher-order difference body and the associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman, Roysdon and Ye expanded the concept to a burgeoning higher-order Brunn-Minkowski theory. In 1991, Zhang introduced mean zonoids of a convex body, which was extended to the Firey-Brunn-Minkowski theory setting by Xi, Guo and Leng in 2014. In this note, we extend these $L^p$ mean zonoids to the higher-order setting and establish the associated isoperimetric inequality. |
| title | General Higher Order $L^p$ Mean Zonoids |
| topic | Metric Geometry Functional Analysis 52A30, 52A40, Secondary: 28A75 |
| url | https://arxiv.org/abs/2312.09500 |