Isotropic surface area measures

Authors
Giannopoulos, A Papadimitrakis, M
Citation
A. Giannopoulos et M. Papadimitrakis, Isotropic surface area measures, MATHEMATIKA, 46(91), 1999, pp. 1-13
Citations number
11
Categorie Soggetti
Mathematics
Journal title
MATHEMATIKA
ISSN journal
00255793 → ACNP
Volume
46
Issue
91
Year of publication
1999
Part
1
Pages
1 - 13
Database
ISI
SICI code
0025-5793(199906)46:91<1:ISAM>2.0.ZU;2-N
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 af fine transformations of the same volume if, and only if, its area measure i s isotropic. We obtain sharp affine inequalities which demonstrate the fact that this "surface isotropic" position is a natural framework for the stud y of hyperplane projections of convex bodies.