This is an announcement for the paper "On the equality conditions of the Brunn-Minkowski theorem" by Daniel A. Klain. Abstract: This article describes a new proof of the equality condition for the Brunn-Minkowski inequality. Archive classification: math.MG math.CA math.FA Mathematics Subject Classification: 52A20, 52A38, 52A39, 52A40 Remarks: 9 pages Submitted from: daniel_klain@uml.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.1409 or http://arXiv.org/abs/1005.1409