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Holomorphic Motions And Extremal Annuli, Zhe Wang

Dissertations, Theses, and Capstone Projects

Holomorphic motions, soon after they were introduced, became an important subject in complex analysis. It is now an important tool in the study of complex dynamical systems and in the study of Teichmuller theory. This thesis serves on two purposes: an expository of the past developments and a discovery of new theories.

First, I give an expository account of Slodkowski's theorem based on the proof given by Chirka. Then I present a result about infinitesimal holomorphic motions. I prove the |ε log ε| modulus of continuity for any infinitesimal holomorphic motion. This proof is a very well application of Schwarz's …