This is an announcement for the paper "Slicing inequalities for measures of convex bodies" by Alexander Koldobsky.

Abstract: We consider a generalization of the hyperplane problem to arbitrary measures in place of volume and to sections of lower dimensions. We prove this generalization for unconditional convex bodies and for duals of bodies with bounded volume ratio. We also prove it for arbitrary symmetric convex bodies under the condition that the dimension of sections is less than $\lambda n$ for some $\lambda\in (0,1).$ The constant depends only on $\lambda.$ Finally, we show that the behavior of the minimal sections for some measures may be different from the case of volume.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 52A20

Submitted from: koldobskiya@missouri.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1412.8550

or

http://arXiv.org/abs/1412.8550