This is an announcement for the paper "Identifying Set Inclusion by Projective Positions and Mixed Volumes" by D.I. Florentin, V. D. Milman, and A. Segal.
Abstract: We study a few approaches to identify inclusion (up to a shift) between two convex bodies in ${\mathbb R}^n$. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or surface area of all projective positions of the sets. We prove similar results for Minkowski sums of the sets.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A05, 52A20, 52A38, 52A39, 51N15, 46B20
Citation: Identifying Set Inclusion by Projective Positions and Mixed
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.03844
or