Lower Bounds on the Low-Distortion Embedding Dimension of Submanifolds of ${\mathbb{R}}^n$

Mark Iwen, Arman Tavakoli, Benjamin Schmidt

Let $\mathcal{M}$ be a smooth submanifold of ${\mathbb{R}}^n$ equipped with the Euclidean (chordal) metric. This note considers the smallest dimension $m$ for which there exists a bi…