5 problems

Convergence conjecture.

Let $M$ be a metric space, let $\operatorname{dens} M$ denote its density, and let $\operatorname{Lip}_0(M)$ be the Banach space of Lipschitz functions on $M$ vanishing at the dist…

The Lipschitz-surface characterization conjecture. The sequence $(x_i)_{i\in I}$ is $d$-controlling if and only if there exist a Lipschitz map $g:\mathbb{R}^d\to\mathbb{R}^m$ and a…

Let $f:{\mathbb{R}}^d\longrightarrow {\mathbb{R}}^m$ be continuous and piecewise Lipschitz with exceptional set $\Theta$. Suppose that $f$ is intrinsically Lipschitz with respect t…

Let $\mathbb{G}$ be a finitely generated group and let $\mu$ be a courteous probability measure on $\mathbb{G}$. Let $\mathsf{LHF}(\mathbb{G},\mu)$ denote the space of Lipschitz…