Discrete subgroups of small critical exponent

It is conjectured by Kapovich that finitely generated Kleinian groups with critical exponent less than 1 are convex-cocompact. In this talk, we partly answer this in the affirmative by showing that any finitely generated Kleinian groups with sufficiently small critical exponent are convex-cocompact. We also give some geometric properties of hyperbolic manifolds with critical exponent less than 1.