4 problems

For a subset $S$ of a metric space $X$, let $\lambda(S,X)$ denote the norm of a bounded linear extension operator from Lipschitz functions on $S$ to Lipschitz functions on $X$, and…

Diameter variation conjecture. For each ropelength level $\Lambda$, there should exist constants $C(\Lambda)>0$ and $\alpha>0$ such that

Non-degeneracy conjecture. The swept-area pseudometric is non-degenerate on each admissible component of $Y_{\Lambda}(K)$ modulo $\operatorname{Isom}^+(\mathbb{R}^3)$: zero swept-a…

Let $X$ be a set and let ${\operatorname{D}}$ be a family of pseudometrics on $X$. The topology induced by ${\operatorname{D}}$ is the topology generated by the pseudometric balls,…