Abstract
We establish the equivalence of some affine isoperimetric inequalities which include the [subscript]Lp[/subscript] -Petty projection inequality, the [subscript]Lp[/subscript] -Busemann-Petty centroid inequality, the "dual" [subscript]Lp[/subscript] -Petty projection inequality, and the "dual" [subscript]Lp[/subscript] -Busemann-Petty inequality. We also establish the equivalence of an affine isoperimetric inequality and its inclusion version for [subscript]Lp[/subscript] -John ellipsoids.
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