Measures on the geometric limit set in higher rank symmetric spaces
by
Gabriele Link
Ecole Polytechnique Palaiseau / University of Karlsruhe

Let G be a discrete group of isometries of a symmetric space X=G/K of noncompact type and rank greater than one. In order to measure the size of the limit set of G in each G-invariant subset of the geometric boundary ¶X, we construct a class of generalized Patterson- Sullivan measures. Introducing an appropriate notion of Hausdorff measure on ¶X, we show how these measures serve as a tool to relate the Hausdorff dimension of the limit set in a given G-invariant subset Y Ì ¶X to the exponential growth rate of orbit points converging towards Y.

Date received: August 30, 2004