Uniform embeddings of hyperbolic groups in Hilbert spaces (Q1802782)

A mapping \(e: A\to B\) between metric spaces \((A,d_ A)\) and \((B,d_ B)\) is said to be a uniform embedding if it is Lipschitz and there exists a function \(\varphi\) with \(\lim \varphi(t)=\infty\) as \(t\to\infty\) such that for all \(x,y\in A\) \(d_ B(e(x),e(y))\geq \varphi(d_ A(x,y))\). The author constructs uniform embeddings of the Cayley graphs of hyperbolic groups and cyclic extensions of torsion-free small cancellation groups in Hilbert spaces.