| Institution: | Department of Mathematics, University of California, Davis, California 95616 E. Lutwak ; Department of Applied Mathematics and Physics, Polytechnic University, Brooklyn, New York 11201 |
| Abstract: | Aleksandrov's projection theorem characterizes centrally symmetric convex bodies by the measures of their orthogonal projections on lower dimensional subspaces. A general result proved here concerning the mixed volumes of projections of a collection of convex bodies has the following corollary. If  is a convex body in  whose projections on  -dimensional subspaces have the same  -dimensional volume as the projections of a centrally symmetric convex body  , then the Quermassintegrals satisfy  , for  , with equality, for any  , if and only if  is a translate of  . The case where  is centrally symmetric gives Aleksandrov's projection theorem. |
