Sharp $L_p$ affine isoperimetric inequalities are established for the entire class of $L_p$ projection bodies and the entire class of $L_p$ centroid bodies. These new inequalities strengthen the $L_p$ Petty projection and the $L_p$ Busemann–Petty centroid inequality.
J. Differential Geom.
83(1):
1-26
(September 2009).
DOI: 10.4310/jdg/1253804349
