Metric Embeddings : Bilipschitz and Coarse Embeddings into Banach Spaces. - Ostrovskii, Mikhail I. (De Gruyter studies in mathematics., 2013)
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poinc.