What happens to a manifold under a bi-Lipschitz map? (Q527443)

The paper is dealing with bi-Lipschitz maps of smooth manifolds in \({\mathbb R}^n\) to \({\mathbb R}^m\). The authors obtain relations between dimension, diameter and other similar characteristics of the manifold and its image. In particular, they study so called reach. For a submanifold \(M\subset {\mathbb R}^n\), the reach \(R\) is the largest number such that the open normal bundle of \(M\) of radius \(r\) is embedded in \({\mathbb R}^n\) for all \(r<R\). The authors establish a lower bound for this characteristic.