The Riemann boundary problem on Riemann surfaces

Yu. L. Rodin

[目次]

  • 1. The Riemann Boundary Problem on Closed Riemann Surfaces.- x1. Riemann Surfaces.- x2. Functions and Differential Forms. Abelian Integrals and Differentials.- x3. Riemann Bilinear Relations. The Riemann - Roch Theorem.- A. Bilinear Relations.- B. A Differential Order.- C. The Riemann - Roch Theorem.- x4. Cauchy-type Integrals.- x5. The Riemann Problem. Number of Solutions.- x6. Inversion of Abelian Integrals and Abel's Theorem. Solvability of the Riemann Problem.- A. Abel's Theorem.- B. Inversion of Abelian Integrals. The Boundary Problem Solvability.- C. Jacobi Variety.- x7. Riemann Theta-Functions. Solvability of the Riemann Boundary Problem.- A. Zeros of the Riemann Theta-Function.- B. The Problem of Inversion of Abelian Integrals.- C. Divisor Classes.- D. The Solvability of the Riemann Problem.- x8. Explicit Formulae for Solutions of the Riemann Problem.- 2. Complex Vector Bundles over Compact Riemann Surfaces.- x9. De Rham and Dolbeault Theorems.- x10. Divisors. Complex Vector Bundles. Serre and Riemann Theorems.- A. Divisors and Complex Line Bundles.- B. The Serre Duality Theorem.- C. The Riemann Theorem.- x11. The Riemann - Roch Theorem. The Riemann Problem.- A. The Riemann - Roch Theorem.- B. Some Corollaries.- C. The Riemann Boundary Problem.- x12. The Second Cousin Problem. Solvability of the Riemann Problem.- A. Characteristic Classes. Abel's Theorem.- B. The Second Cousin Problem.- C. Classification of Complex Line Bundles.- D. Solvability of the Riemann Problem, ? = 0.- E. Solvability of the Riemann Problem, 0 < ? < g.- F. The Nonhomogeneous Riemann Problem.- 3. The Riemann Boundary Problem for Vectors on Compact Riemann Surfaces.- x13. The Riemann Boundary Problem for Vector Functions.- A. The Riemann Problem and Complex Vector Bundles.- B. The General Solution of the Riemann Problem.- C. The Conjugate Problem. The Riemann - Roch Theorem for Vector Bundles.- 4. The Riemann Boundary Problem on Open Riemann Surfaces.- x14. Open Riemann Surfaces.- A. Finite Surfaces.- B. Triviality of Cohomologies on Open Riemann Surfaces.- C. The Riemann Bilinear Relations.- D. The Hodge - Royden Theorem.- x15. D-Cohomologies.- A. D-Cohomology Groups. The Singular Group.- B. Serre Duality.- x16. D-Divisors. The Second Cousin Problem.- A. Divisor Degree.- B. Infinite Divisors.- C. S-Divisors.- D. The Second Cousin Problem.- x17. The Riemann Problem. Solvability.- A. The Problem Statement. The Bundle BG.- B. The Existence of a Solution.- C. The Cauchy Index. The Solvability Conditions.- D. The Case ? = 0. S-Problems.- x18. The Solving of the Riemann Problem in the Explicit Form.- A. Cauchy-type Integrals.- B. Construction of a Solution.- 5. Generalized Analytic Functions.- x19. Bers - Vekua Integral Representations.- A. Generalized Analytic Functions on a Plane.- B. Generalized Analytic Functions on a Compact Riemann Surface. Basic Definitions.- C. The First Bers - Vekua Equation.- D. Equation ??u = Au.- x20. The Riemann - Roch Theorem.- A. Generalized Constants.- B. The Riemann - Roch Theorem.- x21. Nonlinear Aspects of the Generalized Analytic Function Theory.- A. Multiplicative Multivalued Solution. Existence.- B. Multiplicative Constants. Uniqueness.- C. Abel's Theorem.- 6. Integrable Systems.- x22. The Schrodinger Equation.- A. Fast-Decreasing Potentials.- B. Reflection Finite-Zone Potentials.- x23. The Landau - Lifschitz Equation.- A. Fast-Decreasing Potentials.- B. Reflection Finite-Zone Potentials.- x24. Riemann - Hilbert and Related Problems.- A. D-Bar Problem.- B. The Dressing Method.- C. The Riemann-Hilbert Problem.- 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.

「Nielsen BookData」より

この本の情報

書名 The Riemann boundary problem on Riemann surfaces
著作者等 Rodin, I︠U︡riĭ L.
Rodin Y. L.
シリーズ名 Mathematics and its applications
出版元 D.Reidel
刊行年月 c1988
ページ数 xiii, 199 p.
大きさ 25 cm
ISBN 9027726531
NCID BA03459125
※クリックでCiNii Booksを表示
言語 英語
出版国 オランダ
この本を: 
このエントリーをはてなブックマークに追加

Yahoo!ブックマークに登録
この記事をクリップ!
Clip to Evernote
このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想