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

Presents a unified and competitive approach to compact and noncompact Riemann surfaces Includes continuing exercises that run throughout the book and lead to generalizations of the main theorems Will help expand and reinforce a student's knowledge of analysis, geometry, and topology Includes supplementary material: sn.pub/extras

Inhalt

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 R n 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.