A local uniqueness theorem for minimizers of Petty's conjectured projection inequality

Abstract

Employing the inverse function theorem on Banach spaces, we prove that in a $C^2(S^{n-1})$-neighborhood of the unit ball, the only solutions of ${\Pi }^{2}K=cK$ are origin-centered ellipsoids. Here $K$ is an $n$-dimensional convex body, $\Pi K$ is the projection body of $K$ and ${\Pi }^{2}K=\Pi (\Pi K).$

to appear in Mathematika

Cited by in corpus (2)

• Iterations of curvature images
• On the stability of the $L_p$-curvature