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Dual \(L_{p}\) affine isoperimetric inequalities. (English) Zbl 1132.52016

Summary: We establish some inequalities for the dual \(p\)-centroid bodies which are the dual forms of the results by Lutwak, Yang, and Zhang. Further, we establish a Brunn-Minkowski-type inequality for the polar of dual \(p\)-centroid bodies.

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A39 Mixed volumes and related topics in convex geometry
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References:

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