The Riemann Boundary Problem on Riemann Surfaces
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathe...
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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
1988, 1988
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| Edition: | 1st ed. 1988 |
| Series: | Mathematics and its Applications, Soviet Series
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. The Riemann Boundary Problem on Closed Riemann Surfaces
- §1. Riemann Surfaces
- §2. Functions and Differential Forms. Abelian Integrals and Differentials
- §3. Riemann Bilinear Relations. The Riemann — Roch Theorem
- §4. Cauchy-type Integrals
- §5. The Riemann Problem. Number of Solutions
- §6. Inversion of Abelian Integrals and Abel’s Theorem. Solvability of the Riemann Problem
- §7. Riemann Theta-Functions. Solvability of the Riemann Boundary Problem
- §8. Explicit Formulae for Solutions of the Riemann Problem
- 2. Complex Vector Bundles over Compact Riemann Surfaces
- §9. De Rham and Dolbeault Theorems
- §10. Divisors. Complex Vector Bundles. Serre and Riemann Theorems
- §11. The Riemann — Roch Theorem. The Riemann Problem
- §12. The Second Cousin Problem. Solvability of the Riemann Problem
- 3. The Riemann Boundary Problem for Vectors on Compact Riemann Surfaces
- §13. The Riemann Boundary Problem for Vector Functions
- 4. The Riemann Boundary Problem on Open Riemann Surfaces
- §14. Open Riemann Surfaces
- §15. D-Cohomologies
- §16. D-Divisors. The Second Cousin Problem
- §17. The Riemann Problem. Solvability
- §18. The Solving of the Riemann Problem in the Explicit Form
- 5. Generalized Analytic Functions
- §19. Bers — Vekua Integral Representations
- §20. The Riemann — Roch Theorem
- §21. Nonlinear Aspects of the Generalized Analytic Function Theory
- 6. Integrable Systems
- §22. The Schrödinger Equation
- §23. The Landau — Lifschitz Equation
- §24. Riemann — 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 — Hilbert Boundary Problem
- Notations.-References