Euclidean embedding, randomized clustering, and Lipschitz extension for finite and doubling subsets of $L_p$ when $p>2$

Assaf Naor, Kevin Ren

Fix $p>2$. We prove that the Euclidean distortion of every $n$-point subset of $L_p$ is $p^3(\log n{)}^{\frac{1}{2}+o(1)}$, thus, in particular, demonstrating that all $n$-point subsets…