The L₀ Dual John Ellipsoid And Inequality

The ellipsoid is an important geometric research object of integral geometry and convex geometric analysis.With the development of integral geometry and convex geometric analysis,the classical ellipsoid develops to the John ellipsoid?Lp John ellipsoid?the Lewis ellipsoid?the Orlicz-John ellipsoid?the Orlicz-Legendre ellipsoid?the(p,q)-John ellipsoid and so on.The dissertation mainly discusses the L0 dual John ellipsoid and its related geometric inequality.In this paper,we first introduces the research background of the ellipsoid,and then definiens the normalized L0 dual mixed volume.The L0 dual John ellipsoid is introduced by solving a pair of dual optimization problems of the q-th dual curvature measures based on the existing results.The L0 dual John ellipsoid is not only the generalization of the L0 John ellipsoid,but also the case of(p,q)-John ellipsoid at p=0,that is(0,q)-John ellipsoid.Meanwhile,we use the volume relation between the L0 dual John ellipsoid and the(p,q)-John ellipsoid and the(p,q)-Ball's volume-ratio inequality.Analogues of Ball's volume-ratio inequality for the L0 dual John ellipsoid are given.And for the new definition of the star body we get the inclusion about the star body ?-0,q(K,Q)with the star body ?-p,q(K,Q)(0<p??)and the(p,q)-John ellipsoid.