Title: Determining Convex Bodies from Central Sections

Abstract: Barker and Larman posed a problem which asks if a convex body in real n-space is uniquely determined by the volumes of its hyperplane sections supported by an internal compact convex set. A survey of some partial results along with the Minkowski uniqueness theorem are presented along with an outline of a new result which gives an affirmative answer if the section supporting set has positive n-dimensional volume.