An introduction to Riemann surfaces
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L -method, a powerful technique used in the theory of several complex variables. The work features a simple construction of a strictly subharmonic exhaustion function and a related con...
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| 格式: | Livre numérique |
| 語言: | Anglais |
| 出版: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| 版: | 1st ed. 2012. |
| 叢編: | Cornerstones
|
| 主題: | |
| 在線閱讀: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 提示: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to Riemann surfaces, Terrence Napier, Mohan Ramachandran, Boston, Birkhäuser, 2011, 1 vol. (XVII-560 p.), Cornerstones, 978-0-8176-4692-9 • Kolmogorov equations for stochastic PDEs, Giuseppe Da Prato, 2004, Basel, Birkhäuser Verlag, 1 vol. (VII-182 p.), Advanced courses in mathematics, CRM Barcelona, 0-8176-7216-8 |
| 總結: | This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L -method, a powerful technique used in the theory of several complex variables. The work features a simple construction of a strictly subharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such as the Mittag-Leffler, Weierstrass, and Runge theorems; the Riemann Roch theorem; the Serre duality and Hodge decomposition theorems; and the uniformization theorem. The book also contains treatments of other facts concerning the holomorphic, smooth, and topological structure of a Riemann surface, such as the biholomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schönflies theorem (and the Jordan curve theorem), and the existence of smooth structures on second countable surfaces. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course |
|---|---|
| Item Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9780817646936 |
| ISSN: | 2197-1838 |
| 訪問: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |