Strengthened volume inequalities for L_p zonoids of even isotropic measures
arXiv:1608.07084 · doi:10.1090/tran/7299
Abstract
We strengthen the volume inequalities for L_p zonoids of even isotropic measures 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-Lieb inequality for a family of functions that can approximate arbitrary well some Gaussians when equality holds. The special case p=\infty yields a stability version of the reverse isoperimetric inequality for centrally symmetric bodies.