混合相交体的对偶仿射均质积分不等式

The affine quermassintegrals inequalities about the mixed intersection body

Lutwark提出对偶仿射均质积分的概念,拓宽了经典的对偶混合体积理论.混合相交体一直是凸几何经典理论的研究对象,这里结合Hlder积分不等式和Minkowski积分不等式建立了对偶仿射均质积分关于混合相交体的对偶Minkowski不等式和对偶Brunn-Minkowski不等式.

Lutwark introduced the dual affine quermassin-tegrals, expanded the classic theoretics of dual mixed Intersection body. The mixed Intersection body is the objiect to study the Historical Theory of Convex Geometry. By inspiring Holder integral inequality and Minkowski integral inequality, the dual Minkowski inequality and the dual Brunn-Minkowski inequality of the dual affine quermassintegrals were established, which was relate to the mixed.