This is an announcement for the paper "Intersection bodies and generalized cosine transforms" by Boris Rubin.

Abstract: Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. We review some known facts and give them new proofs. The main focus is interrelation between generalized cosine transforms of different kinds and their application to investigation of certain family of intersection bodies, which we call lambda-intersection bodies. The latter include k-intersection bodies (in the sense of A. Koldobsky) and unit balls of finite-dimensional subspaces of $L_p$-spaces. In particular, we show that restriction of the spherical Radon transforms and the generalized cosine transforms onto lower dimensional subspaces preserves their integral-geometric structure. We apply this result to the study of sections of lambda-intersection bodies. A number of new characterizations of this class of bodies and examples are given.

Archive classification:

Mathematics Subject Classification: 44A12; 52A38

Remarks: 36 pages

The source file(s), , is(are) stored in gzipped form as 0704.0061.gz with size 31kb. The corresponding postcript file has gzipped size 195kb.

Submitted from: borisr@math.lsu.edu

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

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

or

http://arXiv.org/abs/

or by email in unzipped form by transmitting an empty message with subject line

uget

or in gzipped form by using subject line

get

to: math@arXiv.org.