Inequalities for mixed intersection bodies (Q2572415)

This paper presents the first systematic study of the properties of mixed intersection bodies which were introduced by Leichtweiß\ in 1998. This work shows also the duality between projections and sections in geometric tomography. The authors first obtain many basic properties (positive homogeneity, multilinearity, nondecreasing monotonicity, preserving linear equivalence in star bodies, \dots) of the mixed intersection operator. Main results are the proof of dual Minkowski inequality, the dual Aleksandrov-Fenchel inequality and the dual Brunn-Minkowski inequality for mixed intersection bodies; at the same time the equality conditions of these inequalities are obtained. An upper bound estimate about mixed intersection bodies is also given. In the proofs, the properties of the spherical Radon transform and some classical integral inequalities play a significative role.