TY - JOUR
T1 - An introduction to the Ribe program
AU - Naor, Assaf
N1 - Funding Information:
Acknowledgements. I am grateful to Larry Guth and Manor Mendel for helpful suggestions. The research presented here is supported in part by NSF grant CCF-0832795, BSF grant 2010021, and the Packard Foundation.
PY - 2012/11
Y1 - 2012/11
N2 - 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.
AB - 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.
KW - bi-Lipschitz and coarse invariants
KW - local theory of Banach spaces
KW - metric embeddings
UR - http://www.scopus.com/inward/record.url?scp=84869210302&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84869210302&partnerID=8YFLogxK
U2 - 10.1007/s11537-012-1222-7
DO - 10.1007/s11537-012-1222-7
M3 - Article
AN - SCOPUS:84869210302
SN - 0289-2316
VL - 7
SP - 167
EP - 233
JO - Japanese Journal of Mathematics
JF - Japanese Journal of Mathematics
IS - 2
ER -