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12:00 pm Wednesday, December 21, 2011 Thesis Defense: The Hopf differential and harmonic maps between branched hyperbolic structuresby Evelyn Lamb in HB427- Let M be a Riemann surface of genus g>1 with fundamental group π. Representations from π to PSL(2,R) occur in 4g-3 components indexed by Euler class. There is one component for each natural number e such that |e| < 2g-1. We use harmonic maps to study representations occurring in the non-maximal components of Hom(PSL(2,R))/PSL(2,R). Specifically, to a branched hyperbolic metric we associate a harmonic map. To this map we associate a quadratic differential φ. We show that the map between branched hyperbolic structures that takes a harmonic map to its Hopf differential φ is injective. This is a partial generalization of Wolf's parametrization of Teichmüller space by harmonic maps.
Submitted by mwolf@rice.edu |