On McMullen's algorithm for the Hausdorff dimension of Complex Schottky Groups

TL;DR

This paper extends McMullen's algorithm to estimate the Hausdorff dimension of limit sets for convex-cocompact subgroups in the complex hyperbolic plane, broadening its applicability in geometric group theory.

Contribution

The authors generalize McMullen's algorithm to complex hyperbolic groups, enabling dimension approximation for a wider class of geometric structures.

Findings

Algorithm successfully approximates Hausdorff dimensions in complex hyperbolic settings.

Extension of McMullen's method to new geometric contexts.

Potential applications in understanding complex hyperbolic group dynamics.

Abstract

We provide a generalization of the McMullen's algorithm to approximate the Hausdorff dimension of the limit set for convex-cocompact subgroups of isometries of the Complex Hyperbolic Plane.