Convex bodies and convexity on grassmann cones (X): Projection functions of parallel convex bodies

Summary It is shown that if K is a convex polyhedron or a smooth convex body, then for sufficiently large positive ρ, the body parallel to K at distance ρ has convex projection functions. An example is given of a convex body which does not have this property. In memory of Guido Castelnuovo, in the recurrence of the first centenary of his birth. Supported by a grant from the National Science Foundation, U.S.A.