A Note on Bézout Type Inequalities for Mixed Volumes and Minkowski Sums

In this note, we study Bézout type inequalities for mixed volumes and Minkowski sums of convex bodies in \({\mathbb {R}}^n\) ${\mathbb{R}}^n$ . We first give a new proof and we extend inequalities of Jian Xiao on mixed discriminants. Then, we use the mass transport method to deduce some Bézout type inequalities for mixed volumes. Finally, we apply these inequalities to obtain Bézout type inequalities for Minkowski sums.