Abstract: Reisner proved a reverse of the Blaschke-Santalo inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santalo inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty’s conjecture for projection bodies, respectively.

Key words: convex body, Blaschke-Santalo inequality, reverse, Petty’s conjecture