The Petty Conjecture for Convex Bodies of Revolution

The Petty conjecture asserts that the quotient \(V_n(ΠK)/V_n(K)^{n-1}\) is minimized among all convex bodies precisely by ellipsoids. In this paper, we prove the conjecture for all convex bodies of revolution in \(\mathbb R^n\), \(n\geq3\), including the equality cases.