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Inequalities for \({L_p}\) mixed intersection bodies. (English) Zbl 1424.52012

Summary: The notions of \({L_p}\) intersection bodies were defined previously. In this paper, we introduce the \({L_p}\) mixed intersection bodies, and establish some geometric inequalities for \({L_p}\) mixed intersection bodies. Furthermore, the Busemann-Petty type problem for \({L_p}\) mixed intersection bodies is shown.

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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