An Introduction to Riemann Surfaces

• Main Authors: Napier, Terrence (Author), Ramachandran, Mohan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
• Series: Cornerstones
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Global analysis (Mathematics).; Manifolds (Mathematics).; Functions of complex variables.; Several Complex Variables and Analytic Spaces.; Global Analysis and Analysis on Manifolds.; Analysis.

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L² -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 co...

Table of Contents:

• 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.