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Analysis Seminar – Geoff Diestel, Texas A&M of Central Texas
December 2, 2016 @ 9:30 am - 10:30 am
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.