An Introduction to Riemann Surfaces

An Introduction to Riemann Surfaces

by Terrence Napier, Mohan Ramachandran


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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.

Product Details

ISBN-13: 9780817646929
Publisher: Birkh�user Boston
Publication date: 09/28/2011
Series: Cornerstones
Edition description: 2012
Pages: 560
Product dimensions: 6.30(w) x 9.20(h) x 1.50(d)

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 ofRiemann Surfaces.-Holomorphic Structures on Topological Surfaces.- Background Material on Analysis in Rnand 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.

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