An Introduction to Riemann Surfaces (Cornerstones) - Hardcover

Napier, Terrence; Ramachandran, Mohan

Hardcover

ISBN 10: 0817646922 ISBN 13: 9780817646929

Verlag: Birkhäuser, 2011

Inhaltsangabe

Preface.- Introduction.- Complex analysis in C.- Riemann Surfaces and the L² \delta-Method for Scalar-Valued Forms.- The L² \delta-Method in a Holomorphic Line Bundle.- Compact Riemann Surfaces.- Uniformization and Embedding of Riemann Surfaces.-Holomorphic Structures on Topological Surfaces.- Background Material on Analysis in Rⁿ and Hilbert Space Theory.- Background Material on Linear Algebra.- Background Material on Manifolds.- Background Material on Fundamental Groups, Covering Spaces, and (Co)homology.- Background Material on Sobolev Spaces and Regularity.- References.- Notation Index.- Subject Index.

Über diesen Titel

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.

Von der hinteren Coverseite

<p>This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the <i>L</i>² -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.  </p><p>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.</p>

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 0817646922
• ISBN 13: 9780817646929
• Einband: Tapa dura
• Anzahl der Seiten: 580
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar