Hausdorff dimension and complex hyperbolic Schottky groups: a simplification.

In the present work, we study the Hausdorff dimension of the limit set of Schottky groups on the boundary of the complex hyperbolic group via the Eigenvalue algorithm as in [17]. The visual geometry on H C 2 ¯ allows a direct application of the Eigenvalue algorithm, but at the same time, it hardens the computations. Using the Heisenberg structure on ∂ H C 2 \ { ∞ } and the Cygan metric, we propose a Markov partition associated with the group that simplifies the application of the Eigenvalue algorithm. [ABSTRACT FROM AUTHOR]