2014/08/24 by Du Zou, Zou, Du, Ge Xiong +1
Mathematics · #52A40 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #math.FA #math.MG #msc:52A40
paper · pdf · doi:10.48550/arxiv.1408.6719
43 Pages
arxiv created 2014/08/24 · arxiv updated 2017/03/14
The Orlicz-Legendre ellipsoids, which are in the framework of emerging dual Orlicz Brunn-Minkowski theory, are introduced for the first time. They are in some sense dual to the recently found Orlicz-John ellipsoids, and have largely generalized the classical Legendre ellipsoid of inertia. Several new affine isoperimetric inequalities are established. The connection between the characterization of Orlicz-Legendre ellipsoids and isotropy of measures is demonstrated.