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Isotropic measure; $L_p$-Petty projection inequality; 𝑝-isoperimetric inequality.

We obtain an isoperimetric inequality which estimate the affine invariant 𝑝-surface area measure on convex bodies. We also establish the reverse version of $L_p$-Petty projection inequality and an affine isoperimetric inequality of $\Gamma_{-p}K$.

Wuyang Yu¹ Gangsong Leng²

1. Institute of Management Decision & Innovation, Hangzhou Dianzi University, Zhejiang 310018, China
2. Department of Mathematics, Shanghai University, Shanghai 200444, China

Published

November 2011

Manuscript received

9 March 2011

Manuscript revised

11 May 2011