Wang, Weidong; Feng, Yibin A general \(L_p\)-version of Petty’s affine projection inequality. (English) Zbl 1283.52008 Taiwanese J. Math. 17, No. 2, 517-528 (2013). 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. Cited in 22 Documents MSC: 52A40 Inequalities and extremum problems involving convexity in convex geometry 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) Keywords:general \(L_p\)-projection body; \(L_p\)-Petty affine projection inequality; \(L_p\)-affine surface area; \(L_p\)-geominimal surface area PDFBibTeX XMLCite \textit{W. Wang} and \textit{Y. Feng}, Taiwanese J. Math. 17, No. 2, 517--528 (2013; Zbl 1283.52008) Full Text: DOI Link