On Ahlfors’ weak finiteness theorem
Hiromi Ohtake · Kyoto journal of mathematics · 1984
5 an d 6 , an d C orollary 4).In §1 we shall define som e notations and state Ahlfors' weak finiteness th e o re m .I n § 2 w e sh all stu d y quasiconformal deformations, a n d derive som e new facts (T heorem s 3 a n d 4).I n § 3 w e s h a ll s ta te o u r main results, w hich w ill be proven in §5, after providing som e lem m as in §4.A nd in the last §6 we shall state som e rem arks for the case n =3, particularly th at o u r class a ( r ) turn s out to b e 0-dimensional.T h e au th o r w ish es to exp ress h is d eep est g ratitu d e to Professor Y. Kusunoki for his encouragement and valuable comments, and for bringing this problem to author's a tte n tio n .A n d th e author also thanks to D rs.M. T aniguchi a n d H . Shiga, a n d M r.M .Masumoto for th eir advices and comments during th e preparation of th is paper.§ 1. Notations and Ahlfors' weak finiteness theorem.