国外数学名著系列59:几何5_在线百科全书查询
国外数学名著系列59:几何5
图书信息
出版社: 科学出版社; 第1版 (2009年1月1日)
外文书名: Geometry Ⅴ Minimal Surfaces
丛书名: 国外数学名著系列（续一）（影印版）59
精装: 272页
正文语种: 英语
开本: 16
ISBN: 9787030235022
条形码: 9787030235022
尺寸: 24 x 17.2 x 2 cm
重量: 581 g
作者简介
作者：(德国)奥斯曼 (R.Osserman)
内容简介
《几何5:最小曲面(影印版59)》 gathers in one plate an overview of some of the most exciting developments, presented by five of the leading contributors to those developments. Hirotaka Fujimoto, who obtained the definitive results on the Gauss map of minimal surfaces, reports on Nevanlinna Theory, and Minimal Surfaces,Stefan Hildebrandt provides an up-to-date account of the Platean problem and related boundary-value problems. David Hoffman arid Hermann Karcher describe the wealth of results on embedded surfaces from the past decade, starting with Costa''s surface and the subsequent Hoffman-Meeks examples. Finally, Leon Simon covers the PDE aspect of minimal surfaces, with a survey of known results both in the classical case of surfaces and in the higher dimensional case, The book will be very useful as a reference and research guide to graduate students and researchers in mathematics.
The theory of minimal surfaces has expanded in many directions over the past decade or two.
目录
1. Introduction
2. Basic Theory and the Global Weierstrass Representation
2.1 Finite Total Curvature
2.2 The Example of Chen-Gackstatter
2.3 Embeddedness and Finite Total Curvature:Necessary Conditions
2.3.1 Flux
2.3.2 Torque
2.3.3 The Halfspace Theorem
2.4 Summary of the Necessary Conditionsfor Existence of Complete Embedded Minimal Surfaces with Finite Total Curvature
3. Examples with Restricted Topology: Existence and Rigidity
3.1 Complete Embedded Minimal Surfaces of Finite Total Curvature and Genus Zero: the Lopez-Ros Theorem
4. Construction of the Deformation Family with Three Ends
4.1 Hidden Conformal Symmetries
4.2 The Birdcage Model
4.3 Meromorphic Functions Constructed by Conformal Mappings
4.3.1 The Function T and Its Relationship to u
4.4 The Function z and the Equation for the Riemann Surface in Terms of z and u
4.5 The Weierstrass Data
4.6 The Logarithmic Growth Rates
4.7 The Period and Embeddedness Problems for the Surfaces Mk,x
4.8 The Details of the Solution of the Period Problem,I. Simplification of the Integrals
4.9 The Details of the Solution of the Period Problem,II. The Monotonicity Lemma
4.9.1 Proof of the Monotonicity Lemma
5. The Structure of the Space of Examples
5.1 The Space of Complete, Embedded Minimal Surfaces of Finite Total Curvature
5.2 Some Questions and Conjectures
6. Finite Total Curvature Versus Finite Topology
6.1 Complete, Properly-Immersed, Minimal Surfaces with More Than One End
6.2 Complete Embedded Minimal Surfaces of Finite Topology and More Than One End
6.3 Complete Embedded Minimal Surfaces of Finite Topology with One End
7. Stability and the Index of the Gauss Map
References
