3 problems

Let $S$ be a surface, and let $\operatorname{Convex}(S)$ denote the space of convex curve functionals on $S$, equipped with the product topology inherited from its values on the cu…

Let $\Sigma$ be a hyperbolic surface, let $\mathcal{L}_{\Sigma}$ be its Liouville current, and let $\operatorname{EL}_{\Sigma}$ denote the continuous extension of extremal length t…

Let $S$ be the underlying surface and let $\mathrm{Flat}(S)$ denote the space of flat metrics on $S$. For $\varphi\in\mathrm{Flat}(S)$, let $L_{\varphi}$ be its Liouville geodesic…