Characterizing unit spheres in Euclidean spaces via reach and volume

Mark Iwen, Benjamin Schmidt, Arman Tavakoli

Let $M$ be a smooth, connected, compact submanifold of ${\mathbb{R}}^n$ without boundary and of dimension $k\ge 2$. Let ${\mathbb{S}}^k\subset {\mathbb{R}}^{k+1}\subset {\mathbb{R}}^n$ d…