New $L_p$ Affine Isoperimetric Inequalities

Abstract

We prove new $L_p$ affine isoperimetric inequalities for all $p\in [-\infty ,1)$. We establish, for all $p\ne -n$, a duality formula which shows that $L_p$ affine surface area of a convex body $K$ equals $L_{\frac{n^2}{p}}$ affine surface area of the polar body $K^{\circ }$.

References in corpus (2)

• Affine maximal hypersurfaces
• Random points, convex bodies, lattices

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