3 problems

For $n\geqslant 2$, let $\Gamma$ be a cocompact lattice of $\operatorname{O}(n,1)$, and let $N\geqslant n$. Consider the standard embedding … A representation is strictly dominated…

Let $\Gamma$ be a convex cocompact subgroup of $\mathrm{PO}(n,1)=\mathrm{Isom}(\mathbb{H}^n)$, where $\mathbb{H}^n$ is real hyperbolic $n$-space. Such a subgroup is noncubulated if…

Barbot's component conjecture. For $p\geq 3$, any $\mathbb{H}^{p,1}$-convex cocompact representation of $\Gamma$ lies in $\mathcal{T}_{\rho_0}$.