Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry

@article{Glorieux2019CriticalEA,
  title={Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry},
  author={Olivier Glorieux and Daniel Monclair},
  journal={International Mathematics Research Notices},
  year={2019}
}
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 set. We show that they are equal and bounded from above by the usual Hausdorff dimension of the limit set. We also prove a rigidity result… 

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