2 problems

Finite-dimensional snowflake embedding conjecture. For every $\upomega\in(0,\tfrac12)$, there exists $\mathsf{C}_\upomega>0$ such that, for every integer $k\geqslant 2$, the…

Let $2<q<p$ and let $\theta\in(0,1)$. The $\theta$-snowflake of $L_q$ is the metric space $(L_q,\|x-y\|_q^\theta)$. Sharp snowflake exponent conjecture. If $(L_q,\|x-y\|_q^\theta)$…