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.
All Science Journal Classification (ASJC) codes
- bi-Lipschitz and coarse invariants
- local theory of Banach spaces
- metric embeddings