The Lp Polar bodies of shadow system and related inequalities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929333734473728 |
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| author | Guo, Lujun Wang, Hanxiao |
| author_facet | Guo, Lujun Wang, Hanxiao |
| contents | The $L_p$ versions of the support function and polar body are introduced by Berndtsson, Mastrantonis and Rubinstein in \cite{Berndtsson-Mastrantonis-Rubinstein-2023} recently. In this paper, we prove that the $L_p$-support function of the shadow system $K_t$ introduced by Rogers and Shephard in \cite{rogers-1958-02,shephard-1964} is convex and the volume of the section of $L_p$ polar bodies of $K_t$ is $\frac{1}{n}$-concave with respect to parameter $t$, and obtain some related inequalities. Finally, we present the reverse Rogers-Shephard type inequality for $L_p$-polar bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Lp Polar bodies of shadow system and related inequalities Guo, Lujun Wang, Hanxiao Functional Analysis 52A40, 52A20, 46G12 The $L_p$ versions of the support function and polar body are introduced by Berndtsson, Mastrantonis and Rubinstein in \cite{Berndtsson-Mastrantonis-Rubinstein-2023} recently. In this paper, we prove that the $L_p$-support function of the shadow system $K_t$ introduced by Rogers and Shephard in \cite{rogers-1958-02,shephard-1964} is convex and the volume of the section of $L_p$ polar bodies of $K_t$ is $\frac{1}{n}$-concave with respect to parameter $t$, and obtain some related inequalities. Finally, we present the reverse Rogers-Shephard type inequality for $L_p$-polar bodies. |
| title | The Lp Polar bodies of shadow system and related inequalities |
| topic | Functional Analysis 52A40, 52A20, 46G12 |
| url | https://arxiv.org/abs/2405.01194 |