Napier / Ramachandran An Introduction to Riemann Surfaces

1. Auflage 2011
ISBN: 978-0-8176-4693-6
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 560 Seiten, eBook

Reihe: Cornerstones

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces.The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course. The prerequisites are a working knowledge of standard topics in graduate level real and complex analysis, and some familiarity of manifolds and differential forms.

Zielgruppe

Graduate

Autoren/Hrsg.

Napier, Terrence

Ramachandran, Mohan

Inhaltsverzeichnis

Preface.- Introduction.- Complex analysis in C .- Riemann Surfaces and the L 2 \delta-Method for Scalar-Valued Forms.- The L 2 \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.