Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916787196526592 |
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| author | Schippers, Eric Staubach, Wolfgang |
| author_facet | Schippers, Eric Staubach, Wolfgang |
| contents | We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of integral operators which we call Schiffer operators, and show that the matrix is unitary. We also obtain a general association of positive polarizing Lagrangian spaces to bordered Riemann surfaces, which unifies the classical polarizations for compact surfaces of algebraic geometry with the infinite-dimensional period map of the universal Teichmüller space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings Schippers, Eric Staubach, Wolfgang Differential Geometry Algebraic Geometry Complex Variables 53C56, 51M15, 30F15, 30F30 We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of integral operators which we call Schiffer operators, and show that the matrix is unitary. We also obtain a general association of positive polarizing Lagrangian spaces to bordered Riemann surfaces, which unifies the classical polarizations for compact surfaces of algebraic geometry with the infinite-dimensional period map of the universal Teichmüller space. |
| title | Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings |
| topic | Differential Geometry Algebraic Geometry Complex Variables 53C56, 51M15, 30F15, 30F30 |
| url | https://arxiv.org/abs/2506.08166 |