Strengthened volume inequalities for L_p zonoids of even isotropic   measures
  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. 
Karoly J. Boroczky, Ferenc Fodor, Daniel Hug
math.PR math.MG