$L_p$ functional Busemann-Petty centroid inequality
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866912271340404736 |
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| author | Haddad, Julian Jimenez, Carlos Hugo da Silva, Leticia Alves |
| author_facet | Haddad, Julian Jimenez, Carlos Hugo da Silva, Leticia Alves |
| contents | If $K\subset\mathbb{R}^n$ is a convex body and $Γ_pK$ is the $p$-centroid body of $K$, the $L_p$ Busemann-Petty centroid inequality states that $\vol(Γ_pK) \geq \vol(K)$, with equality if and only if $K$ is an ellipsoid centered at the origin. In this work, we prove inequalities for a type of functional $r$-mixed volume for $1 \leq r < n$, and establish as a consequence, a functional version of the $L_p$ Busemann-Petty centroid inequality. \keywords{Convex body, Moment body, Busemann-Petty centroid} } |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1906_09599 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $L_p$ functional Busemann-Petty centroid inequality Haddad, Julian Jimenez, Carlos Hugo da Silva, Leticia Alves Functional Analysis Metric Geometry 39B62 If $K\subset\mathbb{R}^n$ is a convex body and $Γ_pK$ is the $p$-centroid body of $K$, the $L_p$ Busemann-Petty centroid inequality states that $\vol(Γ_pK) \geq \vol(K)$, with equality if and only if $K$ is an ellipsoid centered at the origin. In this work, we prove inequalities for a type of functional $r$-mixed volume for $1 \leq r < n$, and establish as a consequence, a functional version of the $L_p$ Busemann-Petty centroid inequality. \keywords{Convex body, Moment body, Busemann-Petty centroid} } |
| title | $L_p$ functional Busemann-Petty centroid inequality |
| topic | Functional Analysis Metric Geometry 39B62 |
| url | https://arxiv.org/abs/1906.09599 |