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Geometry and Analysis(Vol.I)(几何与分析)(第I卷)

样章
作者：
季理真
定价：
88.00元
ISBN：
978-7-04-030272-1
版面字数：
800.000千字
开本：
16开
全书页数：
542页
装帧形式：
精装
重点项目：
暂无
出版时间：
2010-10-08
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：
几何分析

This book contains many substantial papers from distinguishedspeakers of a conference 'Geometric Analysis: Present and Future'and an overview of the works of Professor Shing-Tung Yau.Contributors include E. Wit-ten, Y.T. Siu, R. Hamilton, H. Hitchin,B. Lawson, A. Strominger, C. Vafa, W. Schmid, V. Guillemin, N. Mok,D. Christodoulou. This is a valuable reference that gives anup-to-dated summary of geometric analysis and its applications inmany different areas of mathematics.

  • FrontMatter
  • Part1SummaryofandCommentariesontheWorkofShing-TungYau
  • 0CurriculumVitaeofShing-TungYau
  • 1ABriefOverviewoftheWorkofShing-TungYauLizhenJi
    • 1Introduction
    • 2AsummaryofsomemajorworksofYau
    • 3TopicsYauhasworkedon
    • 4BasicsonKahler-EinsteinmetricsandCalabiconjectures
    • 5SomeapplicationsofKahler-EinsteinmetricsandCalabi-Yaumanifolds
    • 6Harmonicmaps
    • 7RigidityofKahlermanifolds
    • 8Super-rigidityofspacesofnonpositivecurvature
    • 9SurveypapersbyYau
    • 10OpenproblemsbyYau
    • 11Bookswrittenandco-writtenbyYau
    • 12Bookseditedandco-editedbyYau
    • 13Ph.D.studentsofYau
    • 14PartiallistofpapersandbooksofYau
    • References
  • 2Yau'sWorkonFilteringProblemWen-LinChiou,JieHuangandLizhenJi
    • 1Filteringproblem
    • 2Yau'stwomethodsinsolvingnonlinearlteringproblem
      • 2.1Directmethod
      • 2.2Algorithmforrealtimesolutionwithoutmemory
    • References
  • 3FromContinuestoDiscrete—Yau'sWorkonGraphTheoryFanChung
  • 4Yau'sWorkonModuli,Periods,andMirrorMapsforCalabi-YauManifoldsCharlesF.Doran
    • 1ConstructionofCalabi-Yauthreefolds
    • 2Picard-Fuchsequationsandthemirrormap
    • 3Arithmeticpropertiesofmirrormaps
    • 4PeriodsandmoduliofcomplexToriandK3surfaces
    • References
  • 5ReviewonYau'sWorkontheCoupledEinsteinEquationsandtheWaveDynamicsintheKerrGeometryFelixFinster
    • 1CouplingtheEinsteinequationstonon-abeliangaugeeldsandDiracspinors
    • 2ThedynamicsoflinearwavesintheKerrgeometry
    • References
  • 6TheWorkofWittenandYauontheAdS/CFTCorrespondenceGregoryJ.Galloway
    • 1Introduction
    • 2TheWitten-YauresultsonAdS/CFT
    • 3Furtherdevelopments
    • References
  • 7Yau'sWorkonHeatKernelsAlexanderGrigor'yan
    • 1Thenotionoftheheatkernel
    • 2Estimatingheatkernels
    • 3Someapplicationsoftheheatkernelestimates
    • References
  • 8Yau'sContributionstoEngineeringFieldsXianfengDavidGu
    • 1Introduction
    • 2Computationalconformalgeometry
      • 2.1Conformalstructure
      • 2.2Harmonicmap
      • 2.3Surfacericciow
      • 2.4Conformalmappings
      • 2.5Quasi-conformalmappings
      • 2.6Teichmullerspace
    • 3Geometricacquisition
    • 4Computergraphics
    • 5Geometricmodeling
    • 6Medicalimaging
    • 7Computervision
    • 8Wirelesssensornetwork
    • 9Summary
    • References
  • 9TheSYZProposalNaichungConanLeung
    • 1Pre-SYZ
    • 2ThebirthofSYZ
    • 3ThegrowingupofSYZ
      • 3.1SpecialLagrangiangeometry
      • 3.2SpecialLagrangianbrations
      • 3.3Affinegeometry
      • 3.4SYZtransformation
    • 4FutureofSYZ
    • References
  • 10Yau-ZaslowFormulaNaichungConanLeung
  • 11Yau'sWorkonFunctionTheory:HarmonicFunctions,EigenvaluesandtheHeatEquationPeterLi
  • 12AVisionofYauonMirrorSymmetryBongLian
    • 1Enumerativegeometry
    • 2GeometryofCalabi-Yaumanifoldsandtheirmodulispaces
    • References
  • 13Yau'sWorkonGroupActionsKefengLiu
  • 14ChengandYau'sWorkontheMonge-AmpereEquationandAffineGeometryJohnLoftin,Xu-JiaWangandDeaneYang
    • 1Introduction
    • 2TheMonge-Ampereequation
    • 3ChengandYau'sworkontheDirichletproblem
    • 4SubsequentworkontheMonge-Ampereequation
    • 5AffineSpheres
    • 6HyperbolicaffinespheresandrealMonge-Ampereequations
    • 7Afffinemanifolds
    • 8MaximalhypersurfacesinMinkowskispace
    • 9TheMinkowskiproblem
    • 10Convexgeometrywithoutsmoothnessassumptions
      • 10.1Supportfunction
      • 10.2Invariancepropertiesofthesupportfunction
      • 10.3Minkowskisum
      • 10.4Mixedvolume
      • 10.5Surfaceareameasure
      • 10.6Invariancepropertiesofthesurfaceareameasure
      • 10.7TheMinkowskiproblem
      • 10.8TheBrunn-Minkowskiinequality
      • 10.9UniquenessintheMinkowskiproblem
      • 10.10VariationalapproachtotheMinkowskiproblem
    • 11Convexgeometrywithsmoothnessassumptions
      • 11.1TheinverseGaussmap
      • 11.2Theinversesecondfundamentalform
      • 11.3Thecurvaturefunction
      • 11.4Thesurfaceareameasure
      • 11.5TheMinkowskiproblem
      • 11.6TheMinkowskiproblemasaPDE
    • 12ChengandYau'sregularitytheoremfortheMinkowskiproblem
      • 12.1Statement
      • 12.2SketchofProof
    • 13GeneralizationsoftheMinkowskiproblem
    • References
  • 15Yau'sWorkonMinimalSurfacesand3-manifoldsFengLuo
  • 16TheWorkofSchoenandYauonManifoldswithPositiveScalarCurvatureWilliamMinicozziII
    • 0Introduction
    • 1Topologicalrestrictionsonmanifoldswithpositivescalarcurvature
      • 1.1Stableminimalsurfacesandscalarcurvature
      • 1.2Inductivelyextendingthistohigherdimensions
      • 1.3Preservingpositivescalarcurvatureundersurgery
    • 2Locallyconformallyatmanifolds
      • 2.1Thenewinvariants
      • 2.2Apositivemasstheorem
    • References
  • 17Yau'sContributionstoAlgebraicGeometryAndreyTodorov
    • 1Introduction
      • 1.1Yau'sprogram-plenarytalkatICM1982
    • 2Monge-Ampereequationandapplicationstoalgebraicgeometry
      • 2.1SolutionoftheCalabiconjecture
      • 2.2ExistenceofcanonicalmetricsonZariskiopensets
    • 3StablevectorbundlesoverKahlermanifolds
      • 3.1Donaldson-Uhlenbeck-Yautheorem
      • 3.2ApplicationstoKodaira'sclassifficationofsurfaces
    • 4Modulispaces
      • 4.1ExistenceofKahler-EinsteinmetricsondomainofholomorphyandTeichmullerspaces
      • 4.2ModulispacesofK3surfaces
      • 4.3ModulispacesofCYmanifolds
      • 4.4GeneralizationofShwarzlemmabyYauandBaily-Borelcompactification
    • 5ContributionsofYautostringtheory
      • 5.1MirrorsymmetryandSYZconjecture
      • 5.2Largeradiuslimit
      • 5.3Stringtheoryandnumbertheory
      • 5.4RationalcurvesonalgebraicK3surfaces
    • 6Rigidity
      • 6.1Yau'sconjectureaboutrigidityofsomecomplexmanifolds
      • 6.2Geometricproofofmargulis'superrigidity
    • 6.3GeometricproofofKazhdantheoremaboutGaloisconjugationofShimuravarieties
    • References
  • 18Yau'sWorkonPositiveMassTheoremsMu-TaoWang
  • 19Yau'sConjectureonKahler-EinsteinMetricandStabilityXiaoweiWang
  • 20OnYau'sPioneerContributionontheFrankelConjectureandRelatedQuestionsFangyangZheng
  • 21Yau'sWorkonInequalitiesBetweenChernNumbersandUniformizationofComplexManifoldsKangZuo
  • Part2DifferentialGeometryandDifferentialEquations
  • 22GeometryofCompleteGradientShrinkingRicciSolitonsHuai-DongCao
    • 1GradientshrinkingRiccisolitons
    • 2Classificationof3-dimensionalgradientshrinkingsolitons
    • 3Geometryofcompletegradientsolitons
    • References
  • 23TheFormationofBlackHolesinGeneralRelativityDemetriosChristodoulou
  • 24PageRankasaDiscreteGreen'sFunctionFanChung
    • 1Introduction
    • 2Preliminaries
    • 3Dirichleteigenvalues
    • 4ConnectionsbetweenPageRankanddiscreteGreen'sfunction
    • 5RelatingtheCheegerconstanttothePageRank
    • 6RelatingthePageRankofagraphtothatofitssubgraphs
    • 7ThePageRankandthehittingtime
    • References
  • 25AGeodesicEquationintheSpaceofSasakianMetricsPengfeiGuanandXiZhang
  • 26SomeInverseSpectralResultsfortheTwo-dimensionalSchrodingerOperatorV.GuilleminandA.Uribe
    • 1Introduction
    • 2TheWeylcalculus
    • 3Somebracketidentities
    • 4ThequantumBirkhoffcanonicalform
    • References
  • 27Li-YauEstimatesandtheirHarnackInequalitiesRichardS.Hamilton
    • 1Theheatequation
    • 2TheDirichletproblemfortheheatequation
    • 3Theheatequationintheplane
    • 4Thecastaway
    • 5Endangeredspeciesequation
    • 6Themigrationequation
    • 7Motionofacurvebyitscurvature
    • 8Motionofasurfacebyitsmeancurvature
    • 9MotionofasurfacebyitsGausscurvature
    • References
  • 28PlurisubharmonicityinaGeneralGeometricContextF.ReeseHarveyandH.BlaineLawson,Jr
    • 1Introduction
    • 2Geometricallydefinedplurisubharmonicfunctions
    • 3MoregeneralplurisubharmonicfunctionsdefinedbyanellipticconeP+
    • 4P+-plurisubharmonicdistributions
    • 5Upper-semi-continuousP+-plurisubharmonicfunctions
    • 6SomeclassicalfactsthatextendtoP+-plurisubharmonicfunctions
    • 7TheDirichletproblem-uniqueness
    • 8TheDirichletproblem-existence
    • 9P+-convexdomains
    • 10TopologicalrestrictionsonP+-convexdomains
    • 11P+-freesubmanifolds
    • 12P+-convexboundaries
    • References
  • 29PoissonModulesandGeneralizedGeometryNigelHitchin
    • 1Introduction
    • 2Poissonmodules
      • 2.1Definitions
      • 2.2Aconstruction
    • 3TheSerreconstruction
      • 3.1Thealgebraicapproach
      • 3.2Theanalyticalapproach
      • 3.3Thesecondsection
    • 4Generalizedgeometry
      • 4.1Basicfeatures
      • 4.2GeneralizedDolbeaultoperators
      • 4.3Thecanonicalbundle
    • 5Ageneralizedconstruction
      • 5.1Theproblem
      • 5.2Generalizedcomplexsubmanifolds
      • 5.3Theconstruction
    • 6Anapplication
    • References
  • 30UniquenessofSolutionstoMeanFieldEquationsofLiouvilleTypeinTwo-dimensionChang-shouLin
    • 1Introduction
    • 2UniquenessinR2
    • 3UniquenessinboundeddomainsofR2
    • 4Onofriinequalityanditsgeneralization
    • 5MeanfieldequationandGreenfunctionsontorus
    • 6GeneralizedLiouvillesystem
    • References
  • 31MonotonicityandHolomorphicFunctionsLeiNi
  • 32DecayofSolutionstotheCauchyProblemintheKerrGeometryforVariousPhysicalSystems:StabilityofBlackHolesJ.A.Smoller
    • 1Introduction
    • 2Main
    • References
  • 33TheCalabi-YauEquation,SymplecticFormsandAlmostComplexStructuresValentinoTosattiandBenWeinkove
    • 1Background-Yau'sTheorem
    • 2Donaldson'sconjectureandapplications
    • 3EstimatesfortheCalabi-Yauequation
    • 4Methods
    • 5Amonotonicityformula
    • References
  • 34UnderstandingWeil-PeterssonCurvatureScottA.Wolpert
    • 1Introduction
    • 2BasicsofTeichmullertheory
    • 3WPintrinsicgeometry
    • 4Methods
    • 5Applicationsofcurvature
    • 5.1TheworkofLiu,SunandYau
    • 5.2Themodelmetric4dr2+r6d2
    • 5.3Projectionanddistancetoastratum
    • References
  • 35ExamplesofPositivelyCurvedCompleteKahlerManifoldsHung-HsiWuandFangyangZheng
    • 1Introduction
    • 2TheABCDfunctions
    • 3Characterizationbythefunction
    • 4Someexamples
    • 5Characterizationbysurfaceofrevolution
    • 6CorrelationbetweenvolumegrowthandcurvatureDecay
    • References

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