3 problems

Mess's conjecture. There is a unique maximal globally hyperbolic $\mathbb{A}\mathbbm{d}\mathbb{S}^3$ manifold $N$ such that the induced metric on the boundary of the convex core of…

AdS convex-boundary conjecture. There exists a unique globally hyperbolic $\mathbb{A}\mathbbm{d}\mathbb{S}^3$ manifold homeomorphic to $S\times[-1,1]$, with smooth, space-like and…

Let $\rho: \Gamma\to\operatorname{SO}_{0}(2,n)$ be a GHC-regular representation. A representation is quasi-Fuchsian if it is a deformation of the inclusion of a lattice in…