2 problems

Boundary correspondence conjecture. The correspondence between the ideal boundary and the space boundary of polygonal surfaces is the same as in Barbot surfaces.

Let $h_{\mathbf{H}^2}$ be the Hitchin map and let $\sigma_{\mathbf{H}^2}$ be the Hitchin–Li–Mochizuki section, whose image parametrizes quasisymmetric maps associated with the corr…