An Introduction to Riemann Surfaces
Seiten
2011
Birkhauser Boston Inc (Verlag)
978-0-8176-4692-9 (ISBN)
Birkhauser Boston Inc (Verlag)
978-0-8176-4692-9 (ISBN)
This book presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2-method. Exercises are included throughout, which makes this text ideal for a one- or two-semester graduate course.
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.
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.
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.
Reihe/Serie | Cornerstones |
---|---|
Zusatzinfo | 42 Illustrations, black and white; XVII, 560 p. 42 illus. |
Verlagsort | Secaucus |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Schlagworte | complex manifolds • DeRham-Hodge decomposition • Morse Theory • Riemannsche Flächen |
ISBN-10 | 0-8176-4692-2 / 0817646922 |
ISBN-13 | 978-0-8176-4692-9 / 9780817646929 |
Zustand | Neuware |
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