This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS
Lectures on Riemann Surfaces
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Editorial Reviews
Review
O. Forster and B. Gilligan Lectures on Riemann Surfaces "A very attractive addition to the list in the form of a well-conceived and handsomely produced textbook based on several years' lecturing experience . . . This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces. The reviewer is inclined to think that it may well become a favorite."—MATHEMATICAL REVIEWS
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Text: English, German (translation)
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5.0 out of 5 stars
Great book,
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This review is from: Lectures on Riemann Surfaces (Graduate Texts in Mathematics) (Hardcover)
A well presented introduction to the theory of Riemann surfaces. A classic lecture text that I recommend to anyone who needs to know about Riemann surfaces, holomorphic functions and other related algebraic geometry, complex geometry, differential geometry and sheaf cohomology topics.
6 of 11 people found the following review helpful:
4.0 out of 5 stars
Nada mal... (not bad...),
By Jose Javier Zuniga (Peru) - See all my reviews
This review is from: Lectures on Riemann Surfaces (Graduate Texts in Mathematics) (Hardcover)
Buen tratamiento del tema de Superficies de Riemann cerradas y abiertas. Nivel basico y entendible. Recomendable para una primera aproximancion al tema. Viene con ejercicios. Really good book, even for a first aproach to the topic of Riemann Surfaces. You just need basic background but you can also go further if you want. Good set of execises.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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finiteness theorem, algebraic functions, residue theorem, invariant under covering transformations, automorphic behavior, curve lifting property, prescribed principal parts, holomorphic covering map, maximal analytic continuation, countable topology, sheaf axiom, harmonic differential forms, closed discrete subset, meromorphic section, closed differential form, regular boundary point, homotopic curves, sheaf homomorphism, function germ, biholomorphic mapping, local homeomorphism, coordinate neighborhood, closed vector subspace, exact cohomology sequence, universal covering Key Phrases - Capitalized Phrases (CAPs): (learn more)
Compact Riemann Surfaces, Identity Theorem, Abel's Theorem, The Serre Duality Theorem, Weyl's Lemma, Linear Differential Equations, Riemann Mapping Theorem, Dirichlet Problem, The Riemann-Roch Theorem, Riemann's Removable Singularities Theorem, The Exact Cohomology Sequence, The Jacobi Inversion Problem, Differential Forms, The Dirichlet Boundary Value Problem, The Definition of Riemann Surfaces, Maximum Principle, Homotopy of Curves, The Runge Approximation Theorem, Runge's Approximation Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
finiteness theorem, algebraic functions, residue theorem, invariant under covering transformations, automorphic behavior, curve lifting property, prescribed principal parts, holomorphic covering map, maximal analytic continuation, countable topology, sheaf axiom, harmonic differential forms, closed discrete subset, meromorphic section, closed differential form, regular boundary point, homotopic curves, sheaf homomorphism, function germ, biholomorphic mapping, local homeomorphism, coordinate neighborhood, closed vector subspace, exact cohomology sequence, universal covering Key Phrases - Capitalized Phrases (CAPs): (learn more)
Compact Riemann Surfaces, Identity Theorem, Abel's Theorem, The Serre Duality Theorem, Weyl's Lemma, Linear Differential Equations, Riemann Mapping Theorem, Dirichlet Problem, The Riemann-Roch Theorem, Riemann's Removable Singularities Theorem, The Exact Cohomology Sequence, The Jacobi Inversion Problem, Differential Forms, The Dirichlet Boundary Value Problem, The Definition of Riemann Surfaces, Maximum Principle, Homotopy of Curves, The Runge Approximation Theorem, Runge's Approximation Theorem New!
Books on Related Topics Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- Differential Analysis on Complex Manifolds (Graduate Texts in Mathematics, Vol 65) by Raymond O'Neil Wells in Back Matter (1), and Back Matter (2)
- Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis (Encyclopaedia of Mathematical Sciences) by H. Grauert in Front Matter, and Back Matter
- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Back Matter (1), and Back Matter (2)
- Complex Analysis (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), and Back Matter (2)
See all 100 books this book cites
- Complex Variables: An Introduction (Graduate Texts in Mathematics) by Carlos A. Berenstein in Back Matter (1), and Back Matter (2)
- Classical Topics in Complex Function Theory (Graduate Texts in Mathematics) by Reinhold Remmert on page 318, and Back Matter
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Back Matter
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