Purely exponential growth of cusp-uniform actions

  title={Purely exponential growth of cusp-uniform actions},
  author={W. Yang},
  journal={arXiv: Group Theory},
  • W. Yang
  • Published 2016
  • Mathematics
  • arXiv: Group Theory
  • Suppose that a countable group $G$ admits a cusp-uniform action on a hyperbolic space $(X,d)$ such that $G$ is of divergent type. The main result of the paper is characterizing the purely exponential growth type of the orbit growth function by a condition introduced by Dal'bo-Otal-Peign\'e. For geometrically finite Cartan-Hadamard manifolds with pinched negative curvature this condition ensures the finiteness of Bowen-Margulis-Sullivan measures. In this case, our result recovers a theorem of… CONTINUE READING
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