Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry
Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry
Abstract The aim of this article is to understand the geometry of limit sets in pseudo-Riemannian hyperbolic geometry. We focus on a class of subgroups of $\textrm{PO}(p,q+1)$ introduced by Danciger, Guéritaud, and Kassel, called ${\mathbb{H}}^{p,q}$-convex cocompact. We define a pseudo-Riemannian analogue of critical exponent and Hausdorff dimension of the limit …