Schiffer variation of complex structure and coordinates for Teichmüller spaces
This paper concerns the problem of constructing explicit variations of complex structure on a Riemann surface so that the variation parameters provide complex-analytic and real-analytic coordinates for Teichmüller space. It is shown that Schiffer variations at independent points give local coordinates for Teichmüller space. Moreover, it is shown how to generalize this idea to infinite dimensional Teichmüller spaces. The duality between the sequence spaces \(\ell '\) and \(\ell^{\infty}\) corresponds to the duality between integrable cusp forms and bounded cusp forms. Moreover, for a properly chosen countable family of Schiffer variations, a neighborhood of the origin in the sequence space \(\ell^{\infty}\) becomes a local chart for Teichmüller space.
variations of complex structure on a Riemann surface
scientific article; zbMATH DE number 3948729