Circle Packing Theory And A Generalization Of The Classical Schwarz Lemma

Both Ring lemma and Schwarz lemma play very important role in complex analysis, this thesis studies the two lemmas as above. In the ring lemma aspects,basing on M?bius transformation and the Keobe one-quarter theorem, the author present a new proof of Rodin-Sullivan's ring lemma and get a lower bound. This new method is rather elementary and accessible to non-experts. with regard to Schwarz lemma, Basing on the argument principle and homotopy theory, the author extend the classical Schwarz lemma from analytic function to meromorphic function whose number of the zeros are k th, and these functions are defined on the unit disk.