A theorem of Ahlfors for hyperbolic spaces

Su Shing Chen
1978 Transactions of the American Mathematical Society  
L. Ahlfors has proved that if the Dirichlet fundamental polyhedron of a Kleinian group G in the unit ball B3 has finitely many sides, then the normalized Lebesgue measure of L(G) is either zero or one. We generalize this theorem and a theorem of Beardon and Maskit to the n-dimensional case. H". Remark. From the above theorem, we see that the set of approximation points is manageable. Only the parabolic fixed points among the nonapproximation points are well known to us. If the group G has a set
more » ... e group G has a set of nonapproximation points of positive measure, then the Ahlfors theorem fails for that group. According to [2], the limit set L(G) of a purely loxodromic
doi:10.1090/s0002-9947-1978-0496817-0 fatcat:2eece3z2vzb2rdoqxsv4kwcgpa