UNSPECIFIED. (1994) ORBIT COUNTING FOR SOME DISCRETE-GROUPS ACTING ON SIMPLY CONNECTED MANIFOLDS WITH NEGATIVE CURVATURE. INVENTIONES MATHEMATICAE, 117 (2). pp. 275-302. ISSN 0020-9910

Abstract

In this article we develop a method of deriving asymptotic formulae for the orbital counting function for the action of certain discrete groups of isometries of simply connected negatively curved manifolds. We consider the particular case of normal subgroups GAMMA left pointing triangle GAMMA0 of a co-compact group GAMMA0 for which the quotient GAMMA0/GAMMA congruent-to Z(k). Even in the special case of manifolds of constant negative, curvature, this leads to new results. In particular, we have asymptotic estimates for some groups which are not geometrically finite.

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