2 problems

Let $d$ be a convex cone-metric on $S_g$, let $V=V(d)$, and let $P^1=P(d,V,h^1)$ and $P^2=P(d,V,h^2)$ be the convex polyhedral Fuchsian manifold and convex Fuchsian cone-manifold f…

Let $S_g$ be a closed oriented surface of genus $g>1$. A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold homeomorphic to $S_g\times[0,1]$ whose lower boundary…