Institute of Management Decision & Innovation, Hangzhou Dianzi University, Zhejiang 310018, China
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.
We establish the
equivalence of some affine isoperimetric inequalities which include
the -Petty projection inequality, the -Busemann-Petty
centroid inequality, the “dual” -Petty projection inequality,
and the “dual” -Busemann-Petty inequality. We also establish
the equivalence of an affine isoperimetric inequality and its
inclusion version for -John ellipsoids.