A product integral representation of mixed volumes of two convex bodies (Q2858019)

The authors study multiple mixed volumes of \( k \) copies of a convex body in \({\mathbb R}^d\) and \((d-k) \) copies of another convex body, \( d \geq 2\); \( k\geq 1\), \( (d-k) \geq 1\).NEWLINENEWLINEIn terms of the flag measures and generalized principal curvatures, they obtain and investigate integral representations of these mixed volumes and some of their approximations (Theorems 1 and 2). A useful characterization of convex bodies which are summands of a ball is given (Lemma 1). The special case \( d=4\), \(k=2\) is considered in details.