This is an announcement for the paper "From the Brunn-Minkowski inequality to a class of Poincar\'e type inequalities" by Andrea Colesanti. Abstract: We present an argument which leads from the Brunn-Minkowski inequality to a Poincare' type inequality on the boundary of convex bodies with smooth boundary and positive Gauss curvature. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 52A20; 26D10 Remarks: 9 pages The source file(s), testo.tex: 21763 bytes, is(are) stored in gzipped form as 0703584.gz with size 7kb. The corresponding postcript file has gzipped size 93kb. Submitted from: colesant@math.unifi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0703584 or http://arXiv.org/abs/math.FA/0703584 or by email in unzipped form by transmitting an empty message with subject line uget 0703584 or in gzipped form by using subject line get 0703584 to: math@arXiv.org.