The measures of asymmetry for coproducts of convex bodies

Qi Guo, JinFeng Guo and XunLi Su

Vol. 276 (2015), No. 2, 401–418

DOI: 10.2140/pjm.2015.276.401

Abstract

In previous work, we introduced a family of $p$-measures of asymmetry for convex bodies, which have the well-known Minkowski measure of asymmetry as a particular case. We now reveal more properties of $\mathfrak{1}$-measure and $\infty$-measure and give some calculating formulas of $p$-measures, in particular, for the so-called coproducts of convex bodies.

Keywords

Convex bodies, $p$-measure of asymmetry, Mixed volume, Mixed area measure

Mathematical Subject Classification 2010

Primary: 52A20, 52A38, 52A39, 52A40

Milestones

Received: 8 August 2014

Revised: 7 March 2015

Accepted: 19 March 2015

Published: 15 July 2015