7 problems

Elementary molecule conjecture. Every extreme point of $B_{\mathcal{F}(M)}$ is an elementary molecule.

Molecule conjecture. Every extreme point of the unit ball of $\mathcal{F}(M)$ is a molecule $m_{x,y}$ for some distinct $x,y\in M$. This is a central open problem concerning the ex…

Locally flat predual conjecture. Whenever $\mathcal{F}(M)$ is a separable dual, it admits a predual $Y$ consisting entirely of locally flat functions.

Volume-product conjecture for finite metric spaces. One has

Let $M$ be a metric space, let $\mathcal{F}(M)$ be its Lipschitz-free space, and write … for $p\neq q$ in $M$. Such elements are called molecules. Molecule conjecture. Every extrem…

Let $M$ be a complete pointed metric space, and let $\mathcal{F}(M)$ be its Lipschitz-free space. An element of $\mathcal{F}(M)$ is finitely supported if its support is a finite su…

Let $K$ be a countable compact metric space, and let $\mathcal{F}(K)$ denote its Lipschitz-free space. Lipschitz-free space isomorphism conjecture. The space $\mathcal{F}(K)$ shoul…