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Some inequalities for the \(L_p\)-curvature image. (English) Zbl 1187.52010

Summary: Lutwak introduced the notion of \(L_{p}\)-curvature image and proved an inequality for the volumes of a convex body and its \(L_{p}\)-curvature image.
In this paper, we first give a monotonic property of \(L_{p}\)-curvature image. Further, we establish two inequalities for the \(L_{p}\)-curvature image and its polar, respectively. Finally, an inequality for the volumes of \(L_{p}\)-projection body and \(L_{p}\)-curvature image is obtained.

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A38 Length, area, volume and convex sets (aspects of convex geometry)
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References:

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