Special Feature: The 10th Takagi Lectures

Japanese Journal of Mathematics

, Volume 7, Issue 2, pp 167-233

An introduction to the Ribe program

  • Assaf NaorAffiliated withCourant Institute, New York University Email author 

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

Mathematics Subject Classification (2010)

46B07 46B85 46B80