Abstract

Necessary and sufficient conditions are described on ap function Ļ‰ over the unit sphere in Euclideann-spaceE n in order for Ļ‰ 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 1ā‰¦p<nāˆ’1.

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