Dimension of the Limit Set and the Density of Resonances for Convex Co-compact Hyperbolic Surfaces. Acknowledgements. I Should like to Thank Laurent Guillop E and Johannes Sjj Ostrand for Many Stimulating

@inproceedings{ZworskiDimensionOT,
title={Dimension of the Limit Set and the Density of Resonances for Convex Co-compact Hyperbolic Surfaces. Acknowledgements. I Should like to Thank Laurent Guillop E and Johannes Sjj Ostrand for Many Stimulating},
author={M. Zworski}
}

The purpose of this paper is to show how the methods of Sjj ostrand for proving the geometric bounds for the density of resonances 28] apply to the case of convex co-compact hyperbolic surfaces. We prove that the exponent in the Weyl estimate for the number of resonances in subconic neighbourhoods of the continuous spectrum is related to the dimension of the limit set of the corresponding Kleinian group. Figure 1. Tesselation by the Schottky group generated by inversions in three symmetrically… CONTINUE READING