UC Riverside

We investigate properties of the pseudo-Riemannian volume, entropy, and diameter for convex cocompact representations \rho \colon \Gamma \to \mathrm{SO}(p,q+1) of closed p -manifold groups. In particular: We provide a uniform lower bound of the product entropy times volume that depends only on the geometry of the abstract group \Gamma . We prove that the entropy is bounded from above by p-1 with equality if and only if \rho is conjugate to a representation inside \mathrm{S}(\mathrm{O}(p,1)\times\mathrm{O}(q)) , which answers affirmatively to a question of Glorieux and Monclair. Lastly, we prove finiteness and compactness results for groups admitting convex cocompact representations with bounded diameter.