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A general \(L_p\)-version of Petty’s affine projection inequality. (English) Zbl 1283.52008

Summary: About a decade ago, Lutwak, Yang and Zhang introduced the notion of \(L_p\)-projection body. More recently, Wang and Leng established an \(L_p\)-version of Petty’s affine projection inequality. At the same time, Ludwig discovered a family of general \(L_p\)-projection bodies and Haberl and Schuster established Petty’s projection inequality for general \(L_p\)-projection bodies.
In this paper, we establish a general \(L_p\)-version of Petty’s affine projection inequality for general \(L_p\)-projection bodies. Moreover, we obtain an analogous inequality for \(L_p\)-geominimal surface area.

MSC:

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