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

版面字数：

391千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-055636-0

物料号：

55636-00

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

目录
- 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