Determination of convex bodies by certain sets of sectional volumes Original Research Article

Suppose that K and L are convex bodies in Rn with L⊂int K. For each hyperplane H⊂Rn which supports L, define fK,L(H)=|K∩H|, where |·| denotes the n−1-dimensional Lebesgue measure. We conjecture that K is determined uniquely by fK,L. A number of partial results are presented, and some obvious alternative formulations are shown to be trivial.