A threshold phenomenon for embeddings of Euclidean snowflakes and impossibility of dimension reduction

Assaf Naor, Kevin Ren

Fix $0<\theta ⩽1$. We prove that if $1⩽p⩽2/\theta$, then the $\theta$-snowflake of ${\ell }_2^k$, namely, ${\mathbb{R}}^k$ equipped with the metric $((x,y)\in \mathbb{R}^k\t…