L_(0)对偶John椭球

L_(0) Dual John Ellipsoid

椭球是积分几何与凸几何分析中一个重要的几何研究对象,随着积分几何与凸几何分析的发展,椭球也从经典的椭球发展到John椭球、L_(p) John椭球、Lewis椭球、(p,q)-John椭球等.在已有结果的基础上,通过求解关于q-阶对偶曲率测度的对偶极值问题,给出了L_(0)对偶John椭球,它是L_(0) John椭球的推广.

The ellipsoid is an important geometry and convex geometric analysis.With the development of integral geometry and convex geometric analysis,the classical ellipsoid develops to the John ellipsoid,the L_(p) John ellipsoid,the Lewis ellipsoid,the(p,q)-John ellipsoid and so on.In this paper,the L_(0) 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 L_(0) dual John ellipsoid is a generalization of the L_(0) John ellipsoid.