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The purpose of this note is to bring into attention an apparently forgotten result of C. M. Petty: a convex body has minimal surface area among its affine transformations of the same volume if, and only if, its area measure is isotropic. We obtain sharp affine inequalities which demonstrate the fact that this “surface isotropic” position is a natural framework for the study of hyperplane projections of convex bodies.

Let K be an isotropic convex body in R n and let Z q (K) be the L q

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