Author | Rodin, Yu. L. author |
---|---|
Title | The Riemann Boundary Problem on Riemann Surfaces [electronic resource] / by Yu. L. Rodin |
Imprint | Dordrecht : Springer Netherlands, 1988 |
Connect to | http://dx.doi.org/10.1007/978-94-009-2885-5 |
Descript | XIII, 199 p. online resource |
1. The Riemann Boundary Problem on Closed Riemann Surfaces -- ยง1. Riemann Surfaces -- ยง2. Functions and Differential Forms. Abelian Integrals and Differentials -- ยง3. Riemann Bilinear Relations. The Riemann โ Roch Theorem -- ยง4. Cauchy-type Integrals -- ยง5. The Riemann Problem. Number of Solutions -- ยง6. Inversion of Abelian Integrals and Abelโs Theorem. Solvability of the Riemann Problem -- ยง7. Riemann Theta-Functions. Solvability of the Riemann Boundary Problem -- ยง8. Explicit Formulae for Solutions of the Riemann Problem -- 2. Complex Vector Bundles over Compact Riemann Surfaces -- ยง9. De Rham and Dolbeault Theorems -- ยง10. Divisors. Complex Vector Bundles. Serre and Riemann Theorems -- ยง11. The Riemann โ Roch Theorem. The Riemann Problem -- ยง12. The Second Cousin Problem. Solvability of the Riemann Problem -- 3. The Riemann Boundary Problem for Vectors on Compact Riemann Surfaces -- ยง13. The Riemann Boundary Problem for Vector Functions -- 4. The Riemann Boundary Problem on Open Riemann Surfaces -- ยง14. Open Riemann Surfaces -- ยง15. D-Cohomologies -- ยง16. D-Divisors. The Second Cousin Problem -- ยง17. The Riemann Problem. Solvability -- ยง18. The Solving of the Riemann Problem in the Explicit Form -- 5. Generalized Analytic Functions -- ยง19. Bers โ Vekua Integral Representations -- ยง20. The Riemann โ Roch Theorem -- ยง21. Nonlinear Aspects of the Generalized Analytic Function Theory -- 6. Integrable Systems -- ยง22. The Schrรถdinger Equation -- ยง23. The Landau โ Lifschitz Equation -- ยง24. Riemann โ Hilbert and Related Problems -- Appendix 1 Hyperelliptic Surfaces -- Appendix 2 The Matrix Riemann Problem on the Plane -- Appendix 3 One Approximate Method of Solving the Matrix Riemann Problem -- Appendix 4 The Riemann โ Hilbert Boundary Problem -- Notations -- References