An Isometry Theorem for Quadratic Differentials on Riemann Surfaces of Finite Genus

@inproceedings{Laki1997AnIT,
  title={An Isometry Theorem for Quadratic Differentials on Riemann Surfaces of Finite Genus},
  author={Nikola Laki{\vc}},
  year={1997}
}
Assume both X and Y are Riemann surfaces which are subsets of compact Riemann surfaces X1 and Y1, respectively, and that the set X1 −X has infinitely many points. We show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on X and Y are the ones induced by conformal homeomorphisms and complex constants of modulus 1. It follows that every biholomorphic map from the Teichmüller space of X onto the Teichmüller space of Y is… CONTINUE READING

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