Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 981258, 11 pages
doi:10.1155/2009/981258
Research Article

Equivalence of Some Affine Isoperimetric Inequalities

Wuyang Yu

Institute of Management Decision & Innovation, Hangzhou Dianzi University, Zhejiang 310018, China

Received 24 May 2009; Accepted 10 September 2009

Academic Editor: Peter Pang

Copyright © 2009 Wuyang Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish the equivalence of some affine isoperimetric inequalities which include the Lp-Petty projection inequality, the Lp-Busemann-Petty centroid inequality, the “dual” Lp-Petty projection inequality, and the “dual” Lp-Busemann-Petty inequality. We also establish the equivalence of an affine isoperimetric inequality and its inclusion version for Lp-John ellipsoids.