Complex structures in the Nash-Moser category |
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Authors: | Jens Gravesen |
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Affiliation: | (1) Mathematical Institute, The Technical University of Denmark, Building 303, DK-2800 Lyngby, Denmark |
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Abstract: | Working in the Nash-Moser category, it is shown that the harmonic and holomorphic differentials and the Weierstrass points on a closed Riemann surface depend smoothly on the complex structure. It is also shown that the space of complex structures on any compact surface forms a principal bundle over the Teichmüller space and hence that the uniformization maps of the closed disk and the sphere depend smoothly on the complex structure. |
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