This is an announcement for the paper "Non-uniqueness of convex bodies with prescribed volumes of sections and projections" by Fedor Nazarov, Dmitry Ryabogin and Artem Zvavitch.

Abstract: We show that if $d\ge 4$ is even, then one can find two essentially different convex bodies such that the volumes of their maximal sections, central sections, and projections coincide for all directions.

Archive classification: math.CA math.FA math.MG

Mathematics Subject Classification: Primary: 52A20, 52A40, secondary: 52A38

Submitted from: zvavitch@math.kent.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1112.3976

or

http://arXiv.org/abs/1112.3976