  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.
