Strengthened volume inequalities for L_p zonoids of even isotropic measures

摘要

We strengthen the volume inequalities for L_p zonoids of even isotropicmeasures and for their duals, which are due to Ball, Barthe and Lutwak, Yang,Zhang. Along the way, we prove a stronger version of the Brascamp-Liebinequality for a family of functions that can approximate arbitrary well someGaussians when equality holds. The special case p=\infty yields a stabilityversion of the reverse isoperimetric inequality for centrally symmetric bodies.