DUAL $L_{p}$JOHN ELLIPSOIDS.

In this paper, the dual $L_p$John ellipsoids, which include the classical Löwner ellipsoid and the Legendre ellipsoid, are studied. The dual $L_p$versions of Johns inclusion and Balls volume-ratio inequality are shown. This insight allows for a unified view of some basic results in convex geometry and reveals further the amazing duality between Brunn–Minkowski theory and dual Brunn–Minkowski theory. [ABSTRACT FROM AUTHOR]