The Petty Conjecture for Convex Bodies of Revolution

The Petty conjecture asserts that the quotient $V_n(\mathrm{\Pi }K)\mathrm{/}{V}_n(K{)}^{n-1}$ is minimized among all convex bodies precisely by ellipsoids. In this paper, we prove the conjecture for all convex bodies of revolution in ${\mathbb{R}}^n$, $n\ge 3$, including the equality cases.