Campi–Colesanti–Gronchi conjecture for bodies of revolution with constant brightness

Let $b$ be a prescribed brightness, and consider convex bodies of revolution in three-dimensional space with constant brightness $b$. Campi–Colesanti–Gronchi conjecture. The body constructed by Blaschke has minimum volume among all convex bodies of revolution with constant brightness $b$. This is the rotationally symmetric version of the minimum-volume problem for constant brightness; the source gives no resolution.