Resumen de Matheron's conjecture for the covariogram problem

Gabriele Bianchi

• The covariogram of a convex body provides the volumes of the intersections of with all its possible translates. Matheron conjectured in 1986 that this information determines among all convex bodies, up to certain known ambiguities. It is proved that this is the case if is not , or it is not strictly convex, or its boundary contains two arbitrarily small open portions 'on opposite sides'. Examples are also constructed that show that this conjecture is false in for any.