This is an announcement for the paper "An isomorphic version of the slicing problem" by B. Klartag.

Abstract: Here we show that any n-dimensional centrally symmetric convex body K has an n-dimensional perturbation T which is convex and centrally symmetric, such that the isotropic constant of T is universally bounded. T is close to K in the sense that the Banach-Mazur distance between T and K is O(log n). If K has a non-trivial type then the distance is universally bounded. In addition, if K is quasi-convex then there exists a quasi-convex T with a universally bounded isotropic constant and with a universally bounded distance to K.

Archive classification: Metric Geometry; Functional Analysis

Remarks: 19 pages

The source file(s), mixed_MM_star.tex: 44341 bytes, is(are) stored in gzipped form as 0312475.gz with size 13kb. The corresponding postcript file has gzipped size 72kb.

Submitted from: klartagb@post.tau.ac.il

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

http://front.math.ucdavis.edu/math.MG/0312475

or

http://arXiv.org/abs/math.MG/0312475

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

uget 0312475

or in gzipped form by using subject line

get 0312475

to: math@arXiv.org.