Volume inequalities and additive maps of convex bodies
Metric Geometry
2012-08-01 v1 Differential Geometry
Functional Analysis
Abstract
Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary, a new Brunn-Minkowski inequality is obtained for the volume of polar projection bodies.
Keywords
Cite
@article{arxiv.1207.7290,
title = {Volume inequalities and additive maps of convex bodies},
author = {Franz E. Schuster},
journal= {arXiv preprint arXiv:1207.7290},
year = {2012}
}