Japanese Journal of Mathematics

, Volume 7, Issue 2, pp 167–233 | Cite as

An introduction to the Ribe program

Special Feature: The 10th Takagi Lectures


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 embeddings local theory of Banach spaces bi-Lipschitz and coarse invariants 

Mathematics Subject Classification (2010)

46B07 46B85 46B80 


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© The Mathematical Society of Japan and Springer Japan 2012

Authors and Affiliations

  1. 1.Courant Institute, New York UniversityNew YorkUSA

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