9 problems

Let $S$ be a surface, let $\mathcal L(S)$ denote its space of geodesic laminations, and let $d_{\log}$ be the metric on $\mathcal L(S)$ described in the source. Write $\delta$ for…

Let $\Sigma_g$ be a closed surface of genus $g$, let $\sigma\in\mathscr T_g$ be a hyperbolic structure, and let $v$ be a vector in the stretch unit sphere of $T_\sigma\mathscr T_g$…

Daskalopoulos–Uhlenbeck conjecture. For any function of locally least gradient on $\mathbf H^2$, $\mathop{}\!\mathrm{d}u$ should be Ruelle–Sullivan for some, possibly not maximum-s…

Let $u$ be a limit infinity harmonic map between hyperbolic surfaces, and let $\lambda$ be the canonical geodesic lamination with image $\mu$. Non-homeomorphism conjecture. The lim…

The paper constructs dual functions and closed $1$-currents associated with stretch maps, supported on canonical geodesic laminations and valued in the Lie algebra bundle. Geometri…

Let $M$ and $N$ be closed hyperbolic surfaces and fix a homotopy class of maps from $M$ to $N$. Let $\lambda$ be the canonical geodesic lamination associated with the hyperbolic me…

Let $M$ be the surface under consideration and let $\lambda$ be an arbitrary oriented lamination on $M$ with a transverse measure. Let $\tilde v:\tilde M\to\mathbb R$ be a primitiv…

Let $L$ be the flat affine bundle and let $v:M\to L$ be the BV section from Theorem, obtained as a limit of the $q$-harmonic maps. Least-gradient section conjecture. The BV section…

Let $G=\mathrm{PO}(n,1)$, let $\Gamma_0$ be the group in the representation space under consideration, and let $(j,\rho)\in\operatorname{Hom}(\Gamma_0,G)^2$. For $n=2$, assume that…