Discretization and affine approximation in high dimensions
Functional Analysis
2012-02-14 v1 Metric Geometry
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.
Cite
@article{arxiv.1202.2567,
title = {Discretization and affine approximation in high dimensions},
author = {Sean Li and Assaf Naor},
journal= {arXiv preprint arXiv:1202.2567},
year = {2012}
}