Geometric Ruzsa triangle inequality in metric spaces with dilations
arXiv:1304.3358
Abstract
The Appendix of the article arXiv:1212.5056 [math.CO] "On growth in an abstract plane" by Nick Gill, H. A. Helfgott, Misha Rudnev, contains a general "geometric Ruzsa triangle inequality" in a Desarguesian projective plane. The purpose of this note is to give a similar inequality for metric spaces with dilations, that is in the absence of an algebraic or incidence structure.
extended version, detailed proofs, graph rewrites on binary trees used for a short proof of lemma 2