New $L_p$ Affine Isoperimetric Inequalities

Details New $L_p$ Affine Isoperimetric Inequalities New $L_p$ Affine Isoperimetric Inequalities

2007-11-12

arxiv.org/abs/0711.1867v2

Advances in Mathematics, 218 (2008) 762-780

Mathematics

Metric Geometry

Scientific paper

10.1016/j.aim.2008.02.002

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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