Shephard's problem

Shephard's problem refers to a question in the field of convex geometry, specifically related to the properties of convex bodies and their projections. Named after the mathematician G. A. Shephard, the problem explores the relationship between the structure of a convex body in higher-dimensional spaces and the geometric properties of its projections in lower-dimensional spaces. In precise terms, Shephard's problem can be stated about the expected volume or surface area of projections of convex bodies onto lower-dimensional subspaces.