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arXiv · 0711.1867

New $L_p$ Affine Isoperimetric Inequalities

Elisabeth Werner·Deping Ye
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Abstract

We prove new $L_p$ affine isoperimetric inequalities for all $ p \in [-\infty,1)$. We establish, for all $p\neq -n$, 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 $K^\circ$.

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Elisabeth Werner, Deping Ye. 2008-02-22. New $L_p$ Affine Isoperimetric Inequalities. https://doi.org/10.1016/j.aim.2008.02.002

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