幾何V：最小曲面(幾何V：最小曲面)

《幾何V：最小曲面》是2009年1月1日科學出版社出版的圖書，作者是奧斯曼。本書主要講述了關於幾何最小曲面的概念的內涵以及相關研究。

基本介紹

• 書名：幾何V：最小曲面
• 作者：(德國)奧斯曼(R.Osserman)
• ISBN：9787030235022
• 頁數：272頁
• 出版社：科學出版社
• 出版時間：2009年1月1日
• 裝幀：精裝
• 開本：16
• 版次：1

內容簡介

《幾何5:最小曲面(影印版59)》gathersinoneplateanoverviewofsomeofthemostexcitingdevelopments,presentedbyfiveoftheleadingcontributorstothosedevelopments.HirotakaFujimoto,whoobtainedthedefinitiveresultsontheGaussmapofminimalsurfaces,reportsonNevanlinnaTheory,andMinimalSurfaces,StefanHildebrandtprovidesanup-to-dateaccountofthePlateanproblemandrelatedboundary-valueproblems.DavidHoffmanaridHermannKarcherdescribethewealthofresultsonembeddedsurfacesfromthepastdecade,startingwithCosta'ssurfaceandthesubsequentHoffman-Meeksexamples.Finally,LeonSimoncoversthePDEaspectofminimalsurfaces,withasurveyofknownresultsbothintheclassicalcaseofsurfacesandinthehigherdimensionalcase,Thebookwillbeveryusefulasareferenceandresearchguidetograduatestudentsandresearchersinmathematics.Thetheoryofminimalsurfaceshasexpandedinmanydirectionsoverthepastdecadeortwo.

目錄

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