Square integrable harmonic differentials on arbitrary Riemann surfaces with a finite number of nodes (Q1078721)

The paper considers a deformation \((f;R,R_ 0)\) of a Riemann surface \(R_ 0\) with a finite number of nodes to another Riemann surface R and investigates by the deformation induced isomorphism \(H_ f\) between the Hilbert spaces of square integrable differentials \(\Gamma (R_ 0)\) and \(\Gamma\) (R). The estimate of the norm of \(H_ f\) which coincides with the known one when f is a quasiconformal mapping, is given. A certain continuity property of \(H_ f\) on the finitely augmented Teichmüller space of an arbitrary Riemann surface is shown.