McMullen, Curtis T.Ivrii, Oleg2014-06-062014-06-062014Ivrii, Oleg. 2014. The Geometry of the Weil-Petersson Metric in Complex Dynamics. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:11669http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274303In this work, we study an analogue of the Weil-Petersson metric on the space of Blaschke products of degree 2 proposed by McMullen. We show that the Weil-Petersson metric is incomplete and study its metric completion. Our work parallels known results for the Teichmuller space of a punctured torus.en-USMathematicsThesis or Dissertation2014-06-06