On Outer Bi-Lipschitz Extensions of Linear Johnson-Lindenstrauss Embeddings of Low-Dimensional Submanifolds of ${\mathbb{R}}^N$

Mark A. Iwen, Mark Philip Roach

Let $\mathcal{M}$ be a compact $d$-dimensional submanifold of ${\mathbb{R}}^N$ with reach $\tau$ and volume $V_{\mathcal{M}}$. Fix $\epsilon \in (0,1)$. In this paper we prove that a nonlinear f…