Inequalities for Dual Quermassintegrals of Mixed Intersection Bodies

[摘要] In this paper, we first introduce a new concept of dual quermassintegral sum function of two star bodies and establish Minkowski’s type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. Then, we give the Aleksandrov–Fenchel inequality and the Brunn–Minkowski inequality for mixed intersection bodies and some related results. Our results present, for intersection bodies, all dual inequalities for Lutwak’s mixed prosection bodies inequalities.

[学科分类] 数学（综合）

[关键词] Dual mixed volumes;mixed projection bodies;mixed intersection bodies.