4 problems

Let $0<\alpha<1$ and let $n\geq 2$. Equip $\mathbb{R}^n$ with the metric $d_2^\alpha$, where $d_2$ is the metric induced by the standard Euclidean norm, and let…

Let $p,q\in(2,\infty)$ satisfy $q<p$. For $\theta\in(0,1]$, consider the metric space $(L_q,\|x-y\|_{L_q}^\theta)$. Snowflake exponent conjecture. If this metric space admits a bi-…

For $p>2$, let $n$ range over arbitrarily large positive integers, and let $c_{(\mathscr{P}_{p}(\mathbb{R}^3),\mathsf{W}_p)}(Y,d_Y^\alpha)$ denote the least distortion of an embedd…

Let $p\in(2,\infty)$, let $(X,d_X)$ be a finite metric space, and let $c_{(\mathscr{P}_{p}(\mathbb{R}^3),\mathsf{W}_p)}(X,d_X^\alpha)$ denote the least distortion of an embedding o…