2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168911Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.Differential GeometryFunctional Analysis52A40; 52A39text