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Title:
Meromorphic quadratic differentials and geometric structures
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Abstract:
let X be a compact Riemann surface of genus greater than one, and let S denote its underlying smooth surface. Holomorphic quadratic differentials on X parametrize the space of hyperbolic structures, as well as the space of measured foliations, on S. These correspondences between holomorphic objects on one side, and certain geometric structures on the other, are theorems of Wolf and Hubbard-Masur, respectively. I shall discuss these, and talk of their generalizations to the case of a punctured surface when the quadratic differential has poles of higher order. The proofs involve the theory of harmonic maps between surfaces, and in particular, infinite-energy maps that arise in degenerations of the usual correspondence. Part of this work is joint with Michael Wolf
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