English

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}
}