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Isotropic surface area measures

Published online by Cambridge University Press:  26 February 2010

A. Giannopoulos
Affiliation:
Department of Mathematics, University of Crete, Iraklion, Crete, Greece. e-mail: deligia@talos.cc.uch.gr
M. Papadimitrakis
Affiliation:
Department of Mathematics, University of Crete, Iraklion, Crete, Greece. e-mail: papadim@talos.cc.uch.gr
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Abstract

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.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1999

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