Compact Riemann surfaces : an introduction to contemporary mathematics

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Compact Riemann surfaces : an introduction to contemporary mathematics / Jürgen Jost

版:: 2nd ed
資料種別:: 図書
出版情報:: Berlin ; Tokyo : Springer, c2002
形態:: xvi, 278 p. ; 24 cm
シリーズ名:: Universitext <BA00021004>
著者名:: Jost, Jürgen, 1956- <DA01177140>
ISBN:: 9783540432999 [354043299X]
書誌ID:: BA56942983

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他の版・巻

Compact Riemann surfaces : an introduction to contemporary mathematics (: pbk)
Jürgen Jost ; translated by R.R. Simha , Springer , c1997

書誌詳細

その他の標題:

Riemannsche Flächen

注記:

Includes bibliographical references (p. [271]-272) and index

主題:

Riemann surfaces

言語:

英語

目次情報:

Preface

Topological Foundations / 1：

Manifolds and Di erentiable Manifolds / 1.1：

Homotopy of Maps. The Fundamental Group / 1.2：

Coverings / 1.3：

Global Continuation of Functions on Simply-Connected Manifolds / 1.4：

Di erential Geometry of Riemann Surfaces / 2：

The Concept of a Riemann Surface / 2.1：

Some Simple Properties of Riemann Surfaces / 2.2：

Metrics on Riemann Surfaces / 2.3：

Triangulations of Compact Riemann Surfaces / 2.3.A：

Discrete Groups of Hyperbolic Isometries. Fundamental Polygons. Some Basic Concepts of Surface Topology and Geometry / 2.4：

The Topological Classi cation of Compact Riemann Surfaces / 2.4.A：

The Theorems of Gauss-Bonnet and Riemann-Hurwitz / 2.5：

A General Schwarz Lemma / 2.6：

Conformal Structures on Tori / 2.7：

Harmonic Maps / 3：

Review: Banach and Hilbert Spaces. The Hilbert Space L2 / 3.1：

The Sobolev Space W 1; 2 = H1; 2 / 3.2：

The Dirichlet Principle. Weak Solutions of the Poisson Equation / 3.3：

Harmonic and Subharmonic Functions / 3.4：

The C -Regularity Theory / 3.5：

Maps Between Surfaces. The Energy Integral. De nition and Simple Properties of Harmonic Maps / 3.6：

Existence of Harmonic Maps / 3.7：

Regularity of Harmonic Maps / 3.8：

Uniqueness of Harmonic Maps / 3.9：

Harmonic Di eomorphisms / 3.10：

Metrics and Conformal Structures / 3.11：

Teichmuller Spaces / 4：

The Basic De nitions / 4.1：

Harmonic Maps, Conformal Structures and Holomorphic Quadratic Di erentials. TeichmullerÃ†s Theorem / 4.2：

Fenchel-Nielsen Coordinates. An Alternative Approach to the Topology of Teichmuller Space / 4.3：

Uniformization of Compact Riemann Surfaces / 4.4：

Geometric Structures on Riemann Surfaces / 5：

Preliminaries: Cohomology and Homology Groups / 5.1：

Harmonic and Holomorphic Di erential Forms on Riemann Surfaces / 5.2：

The Periods of Holomorphic and Meromorphic Di erential Forms / 5.3：

Divisors. The Riemann-Roch Theorem / 5.4：

Holomorphic 1-Forms and Metrics on Compact Riemann Surfaces / 5.5：

Divisors and Line Bundles / 5.6：

Projective Embeddings / 5.7：

Algebraic Curves / 5.8：

AbelÃ†s Theorem and the Jacobi Inversion Theorem / 5.9：

Elliptic Curves / 5.10：

Sources and References

Bibliography

Index of Notation

Index

Preface

Topological Foundations / 1：

Manifolds and Di erentiable Manifolds / 1.1：

Homotopy of Maps. The Fundamental Group / 1.2：

Coverings / 1.3：

Global Continuation of Functions on Simply-Connected Manifolds / 1.4：

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