Intermediate christoffel-minkowski problems for figures of revolution

Necessary and sufficient conditions are described on ap function ω over the unit sphere in Euclideann-spaceE ⁿ in order for ω to be thepth order, elementary symmetric function of the prncipal radii on the boundary of a sufficiently smooth convex body of revolution inE ⁿ ; here these radii are taken as functions of the outer unit normal direction on the bounding surface;p satisfies 1≦p<n−1.