| Let Gamma be a non-elementary Kleinian group and epsilon > 0. We prove the existence of a Schottky subgroup G&d5; of Gamma so that its critical exponent delta( G&d5; ) < epsilon. Since Schottky groups are geometrically finite, delta( G&d5; ) = dim(Lambda( G&d5; )) and hence dim(Lambda( G&d5; )) < epsilon. Furthermore, we prove the existence of an infinitely generated subgroup G&d14; of Gamma so that delta( G&d14; ) < epsilon. However, G&d14; is not geometrically finite so delta( G&d14; ) may not equal dim(Lambda( G&d14; )). The construction of G&d14; is examined in order to prove an upper bound for dim(Lambda( G&d14; )). As a consequence, given a sequence {Gammai} of Kleinian groups with a uniform porosity constant that converges geometrically to Gamma infinity we obtain conditions on the sequence which guarantee that Gamma infinity is porous. |
