Fourier transform and \(L_{p}\)-mixed centroid bodies (Q2883210)
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scientific article; zbMATH DE number 6033561
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier transform and \(L_{p}\)-mixed centroid bodies |
scientific article; zbMATH DE number 6033561 |
Statements
11 May 2012
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centroid body
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Busemann-Petty problem
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Fourier transform
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mixed curvature function
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quermassintegrals
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0.9315307
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0.88643175
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0.8718029
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0.8694948
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0.86511546
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0.8638274
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Fourier transform and \(L_{p}\)-mixed centroid bodies (English)
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In the Brunn-Minkowski theory and the dual Brunn-Minkowski theory, also centroid bodies of given convex bodies play an essential role. In the present paper, the authors investigate a generalization of this notion. Introducing the concept of \(L_p\)-mixed centroid bodies and variants thereof, they study a Busemann-Petty type problem for two given convex bodies \(K\) and \(L\). The results refer to containments of respective variants of centroid bodies and corresponding inequalities following for the corresponding quermassintegrals of \(K\) and \(L\).
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