Japanese Journal of Mathematics

, Volume 7, Issue 2, pp 167–233

An introduction to the Ribe program

Special Feature: The 10th Takagi Lectures

DOI: 10.1007/s11537-012-1222-7

Cite this article as:
Naor, A. Jpn. J. Math. (2012) 7: 167. doi:10.1007/s11537-012-1222-7

Abstract

We survey problems, results, ideas, and recent progress in the Ribe program. The goal of this research program, which is motivated by a classical rigidity theorem of Martin Ribe, is to obtain structural results for metric spaces that are inspired by the local theory of Banach spaces. We also present examples of applications of the Ribe program to several areas, including group theory, theoretical computer science, and probability theory.

Keywords and phrases

metric embeddingslocal theory of Banach spacesbi-Lipschitz and coarse invariants

Mathematics Subject Classification (2010)

46B0746B8546B80

Copyright information

© The Mathematical Society of Japan and Springer Japan 2012

Authors and Affiliations

  1. 1.Courant Institute, New York UniversityNew YorkUSA