复分析：几何观点，第二版（影印版）

样章

作者：

Steven G. Krantz

定价：

99.00元

ISBN：

978-7-04-055636-0

版面字数：

391.000千字

开本：

特殊

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

出版时间：

2021-03-01

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

前辅文
0 Principal Ideas of Classical Function Theory
- 1. A Glimpse of Complex Analysis
- 2. The Maximum Principle, the Schwarz Lemma, and Applications
- 3. Normal Families and the Riemann Mapping Theorem
- 4. Isolated Singularities and the Theorems of Picard
1 Basic Notions of Differential Geometry
- 0. Introductory Remarks
- 1. Riemannian Metrics and the Concept of Length
- 2. Calculus in the Complex Domain
- 3. Isometries
- 4. The Poincaré Metric
- 5. The Schwarz Lemma
- 6. A Detour into Non-Euclidean Geometry
2. Curvature and Applications
- 1. Curvature and the Schwarz Lemma Revisited
- 2. Liouville's Theorem and Other Applications
- 3. Normal Families and the Spherical Metric
- 4. A Generalization of Montel's Theorem and the Great Picard Theorem
3 Some New Invariant Metrics
- 0. Introductory Remarks
- 1. The Carathéodory Metric
- 2. The Kobayashi Metric
- 3. Completeness of the Carathéodory and Kobayashi Metrics
- 4. An Application of Completeness: Automorphisms
- 5. Hyperbolicity and Curvature
4 Introduction to the Bergman Theory
- 0. Introductory Remarks
- 1. Bergman Basics
- 2. Invariance Properties of the Bergman Kernel
- 3. Calculation of the Bergman Kernel
- 4. About the Bergman Metric
- 5. More on the Bergman Metric
- 6. Application to Conformal Mapping
5 A Glimpse of Several Complex Variables
- 0. Functions of Several Complex Variables
- 1. Basic Concepts
- 2. The Automorphism Groups of the Ball and Bidisc
- 3. Invariant Metrics and the Inequivalence of the Ball and the Bidisc
Appendix
- 1. Introduction
- 2. Expressing Curvature Intrinsically
- 3. Curvature Calculations on Planar Domains
Symbols
References
Index