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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.…mehr

Produktbeschreibung
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.

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• Produktdetails
• Verlag: Springer Basel AG
• Seitenzahl: 560
• Erscheinungstermin: 8. September 2011
• Englisch
• ISBN-13: 9780817646936
• Artikelnr.: 37344410
Inhaltsangabe
From the 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.
Rezensionen
From the reviews:

"The present book gives a solid introduction to the theory of both compact and non-compact Riemann surfaces. While modern introductions often take the view point of algebraic geometry, the present book tries to also cover the analytical aspects. ... The book is well written and constitutes a nice contribution to the existing literature on this topic." (G. Teschl, Internationale Mathematische Nachrichten, Issue 225, 2014)

"This book takes the point of view that Riemann surface theory lies at the root of much of modern analysis, and ... illustrate some of the interactions of analysis with geometry and topology. ... While much of the book is intended for students at the second-year graduate level, Chapters 1 and 2 and Section 5.2 (along with the required background material) could serve as the basis for the complex analytic analysis component of a year-long first-year graduate-level course on real and complex analysis." (V. V. Chueshev, Zentralblatt MATH, Vol. 1237, 2012)