On the Koebe-Maskit theorem
Takehiko Sasaki · Tohoku Mathematical Journal · 1981
Introduction.Let G be a finitely generated Kleinian group and denote by {JJ the set of all components of G.In [3], Maskit showed the convergence of the series ΣDIA 4 ^), where DIA(4) denotes the spherical diameter of Δ t and Σ is taken over all components of G.We shall call this result the Koebe-Maskit theorem.In his proof it is shown that if there is no parabolic element in G, then ΣDIA 2 (4) 2, then Σ DIA« (4) < -, where Σ ^s taken over all components of G.