This is an announcement for the paper "Discretization and affine approximation in high dimensions" by Sean Li and Assaf Naor.

Abstract: Lower estimates are obtained for the macroscopic scale of affine approximability of vector-valued Lipschitz functions on finite dimensional normed spaces, completing the work of Bates, Johnson, Lindenstrass, Preiss and Schechtman. This yields a new approach to Bourgain's discretization theorem for superreflexive targets.

Archive classification: math.FA math.MG

Submitted from: naor@cims.nyu.edu

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

http://front.math.ucdavis.edu/1202.2567

or

http://arXiv.org/abs/1202.2567