国外数学名著系列（续1）（影印版）59：几何5（最小曲面）

图书标准信息

• 作者 [德]奥斯曼 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030235022
• 定价 66.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 272页
• 字数 343千字
• 正文语种 英语
• 丛书 国外数学名著系列:59

【内容简介】

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

【目录】

1.Introduction
2.BasicTheoryandtheGlobalWeierstrassRepresentation
2.1FiniteTotalCurvature
2.2TheExampleofChen-Gackstatter
2.3EmbeddednessandFiniteTotalCurvature：NecessaryConditions
2.3.1Flux
2.3.2Torque
2.3.3TheHalfspaceTheorem
2.4SummaryoftheNecessaryConditionsforExistenceofCompleteEmbeddedMinimalSurfaceswithFiniteTotalCurvature

3.ExampleswithRestrictedTopology：ExistenceandRigidity
3.1CompleteEmbeddedMinimalSurfacesofFiniteTotalCurvatureandGenusZero：theLopez-RosTheorem

4.ConstructionoftheDeformationFamilywithThreeEnds
4.1HiddenConformalSymmetries
4.2TheBirdcageModel
4.3MeromorphicFunctionsConstructedbyConformalMappings
4.3.1TheFunctionTandItsRelationshiptou
4.4TheFunctionzandtheEquationfortheRiemannSurfaceinTermsofzandu
4.5TheWeierstrassData
4.6TheLogarithmicGrowthRates
4.7ThePeriodandEmbeddednessProblemsfortheSurfacesMk，x
4.8TheDetailsoftheSolutionofthePeriodProblem，I.SimplificationoftheIntegrals
4.9TheDetailsoftheSolutionofthePeriodProblem，II.TheMonotonicityLemma
4.9.1ProofoftheMonotonicityLemma

5.TheStructureoftheSpaceofExamples
5.1TheSpaceofComplete，EmbeddedMinimalSurfacesofFiniteTotalCurvature
5.2SomeQuestionsandConjectures

6.FiniteTotalCurvatureVersusFiniteTopology
6.1Complete，Properly-Immersed，MinimalSurfaceswithMoreThanOneEnd
6.2CompleteEmbeddedMinimalSurfacesofFiniteTopologyandMoreThanOneEnd
6.3CompleteEmbeddedMinimalSurfacesofFiniteTopologywithOneEnd
7.StabilityandtheIndexoftheGaussMap
References