\(L_p\) centroid bodies with respect to weights \(|x|^{\ell}\) (Q6097704)
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scientific article; zbMATH DE number 7693165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L_p\) centroid bodies with respect to weights \(|x|^{\ell}\) |
scientific article; zbMATH DE number 7693165 |
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\(L_p\) centroid bodies with respect to weights \(|x|^{\ell}\) (English)
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7 June 2023
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The main result is an isoperimetric inequality for origin-symmetric convex bodies \(K\subset \mathbb{R}^n\) involving the weighted volume of \(K\) with the power weight \(|x|^\ell\) and the corresponding weighted polar \(L_p\) centroid body. A functional version of the weighted polar \(L_p\) Busemann-Petty centroid inequality is obtained.
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centroid bodies
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polar Busemann-Petty centroid inequality
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Blaschke-Santaló inequality
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weighted isoperimetric inequality
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