Complex hyperbolic Kleinian groups of large critical exponents

Abstract

In this article, we show that there exist discrete isometry groups of the $2$- and $3$-dimensional complex hyperbolic spaces with critical exponents arbitrarily close to but strictly smaller than the maximum possible value. This result shows no gap in the values of critical exponents for complex hyperbolic Kleinian groups.

arXiv comment8 pages. We improved the main results. Accepted by J. Differential Geom