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丛书简介
力学基础与工程技术前沿
Geometry and Analysis(Vol.I)(几何与分析)(第I卷)
作 者:
季理真
ISBN:978-7-04-030272-1 出版时间:2010-10-08
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FrontMatter
Part1SummaryofandCommentariesontheWorkofShing-TungYau
0CurriculumVitaeofShing-TungYau
1ABriefOverviewoftheWorkofShing-TungYauLizhenJi
2Yau'sWorkonFilteringProblemWen-LinChiou,JieHuangandLizhenJi
3FromContinuestoDiscrete—Yau'sWorkonGraphTheoryFanChung
4Yau'sWorkonModuli,Periods,andMirrorMapsforCalabi-YauManifoldsCharlesF.Doran
5ReviewonYau'sWorkontheCoupledEinsteinEquationsandtheWaveDynamicsintheKerrGeometryFelixFinster
6TheWorkofWittenandYauontheAdS/CFTCorrespondenceGregoryJ.Galloway
7Yau'sWorkonHeatKernelsAlexanderGrigor'yan
8Yau'sContributionstoEngineeringFieldsXianfengDavidGu
9TheSYZProposalNaichungConanLeung
10Yau-ZaslowFormulaNaichungConanLeung
11Yau'sWorkonFunctionTheory:HarmonicFunctions,EigenvaluesandtheHeatEquationPeterLi
12AVisionofYauonMirrorSymmetryBongLian
13Yau'sWorkonGroupActionsKefengLiu
14ChengandYau'sWorkontheMonge-AmpereEquationandAffineGeometryJohnLoftin,Xu-JiaWangandDeaneYang
15Yau'sWorkonMinimalSurfacesand3-manifoldsFengLuo
16TheWorkofSchoenandYauonManifoldswithPositiveScalarCurvatureWilliamMinicozziII
17Yau'sContributionstoAlgebraicGeometryAndreyTodorov
18Yau'sWorkonPositiveMassTheoremsMu-TaoWang
19Yau'sConjectureonKahler-EinsteinMetricandStabilityXiaoweiWang
20OnYau'sPioneerContributionontheFrankelConjectureandRelatedQuestionsFangyangZheng
21Yau'sWorkonInequalitiesBetweenChernNumbersandUniformizationofComplexManifoldsKangZuo
Part2DifferentialGeometryandDifferentialEquations
22GeometryofCompleteGradientShrinkingRicciSolitonsHuai-DongCao
23TheFormationofBlackHolesinGeneralRelativityDemetriosChristodoulou
24PageRankasaDiscreteGreen'sFunctionFanChung
25AGeodesicEquationintheSpaceofSasakianMetricsPengfeiGuanandXiZhang
26SomeInverseSpectralResultsfortheTwo-dimensionalSchrodingerOperatorV.GuilleminandA.Uribe
27Li-YauEstimatesandtheirHarnackInequalitiesRichardS.Hamilton
28PlurisubharmonicityinaGeneralGeometricContextF.ReeseHarveyandH.BlaineLawson,Jr
29PoissonModulesandGeneralizedGeometryNigelHitchin
30UniquenessofSolutionstoMeanFieldEquationsofLiouvilleTypeinTwo-dimensionChang-shouLin
31MonotonicityandHolomorphicFunctionsLeiNi
32DecayofSolutionstotheCauchyProblemintheKerrGeometryforVariousPhysicalSystems:StabilityofBlackHolesJ.A.Smoller
33TheCalabi-YauEquation,SymplecticFormsandAlmostComplexStructuresValentinoTosattiandBenWeinkove
34UnderstandingWeil-PeterssonCurvatureScottA.Wolpert
35ExamplesofPositivelyCurvedCompleteKahlerManifoldsHung-HsiWuandFangyangZheng
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
29PoissonModulesandGeneralizedGeometryNigelHitchin
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