A unitary scattering matrix for harmonic one-forms on Riemann surfaces is constructed from Schiffer operators, and its associated polarizations unify the classical and universal Teichmüller period maps.
Scattering theory on Riemann surfaces I: Schiffer operators, cohomol- ogy, and index theorems
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Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings
A unitary scattering matrix for harmonic one-forms on Riemann surfaces is constructed from Schiffer operators, and its associated polarizations unify the classical and universal Teichmüller period maps.