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Isotropic surface area measures

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

A. Giannopoulos  and
M. Papadimitrakis
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

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 1 - 13
Copyright
Copyright © University College London 1999

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