This is an announcement for the paper "Brunn-Minkowski and Zhang inequalities for convolution bodies" by David Alonso-Gutierrez, C. Hugo Jimenez, and Rafael Villa.
Abstract: A quantitative version of Minkowski sum, extending the definition of $\theta$-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties on Convex Geometry involving convolution bodies or polar projection bodies. The extension of this new version to more than two sets is also given.
Archive classification: math.FA
Mathematics Subject Classification: 52A40 (Primary), 52A20, 52A23 (Secondary)
Remarks: 16 pages
Submitted from: carloshugo@us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.4757
or