紧黎曼曲面

图书标准信息

• 作者 [德]乔斯特 著
• 出版社 世界图书出版公司
• 出版时间 2009-06
• 版次 1
• ISBN 9787510004728
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 277页
• 正文语种 英语

【内容简介】

UniformizationofCompactRiemannSurfacesGeometricStructuresonRiemannSurfaces、Preliminaries：CohomologyandHomologyGroups、HarmonicandHolomorphicDifferentialFormsonRiemannSurfaces、ThePeriodsofHolomorphicandMeromorphicDifferentialForms、Divisors.TheRiemann-RochTheorem、Holomorphic1-FormsandMetricsonCompactRiemannSurfaces、DivisorsandLineBundles等。

【作者简介】

作者：(德国)乔斯特(Jost.J.)

【目录】

Preface
1TopologicalFoundations
1.1ManifoldsandDifferentiableManifolds
1.2HomotopyofMaps.TheFundamentalGroup
1.3Coverings
1.4GlobalContinuationofFunctionsonSimply-ConnectedManifolds
2DifferentialGeometryofRiemannSurfaces
2.1TheConceptofaRiemannSurface
2.2SomeSimplePropertiesofRiemannSurfaces
2.3MetricsonRiemannSurfaces
2.3ATriangulationsofCompactRiemannSurfaces
2.4DiscreteGroupsofHyperbolicIsometries.FundamentalPolygons.SomeBasicConceptsofSurfaceTopologyandGeometry.
2.4ATheTopologicalClassificationofCompactRiemannSurfaces
2.5TheTheoremsofGauss-BonnetandRiemann-Hurwitz
2.6AGeneralSchwarzLemma
2.7ConformalStructuresonTori
3HarmonicMaps
3.1Review:BanachandHilbertSpaces.TheHilbertSpaceL2
3.2TheSobolevSpaceW12=H12
3.3TheDirichletPrinciple.WeakSolutionsofthePoissonEquation
3.4HarmonicandSubharmonicFunctions
3.5TheCaRegularityTheory
3.6MapsBetweenSurfaces.TheEnergyIntegral.DefinitionandSimplePropertiesofHarmonicMaps
3.7ExistenceofHarmonicMaps
3.8RegularityofHarmonicMaps
3.9UniquenessofHarmonicMaps
3.10HarmonicDiffeomorphisms
3.11MetricsandConformalStructures
4TeichmullerSpaces
4.1TheBasicDefinitions
4.2HarmonicMaps,ConformalStructuresandHolomorphicQuadraticDifferentials.TeichmiillersTheorem
4.3Fenchel-NielsenCoordinates.AnAlternativeApproachtotheTopologyofTeichmiillerSpace
4.4UniformizationofCompactRiemannSurfacesGeometricStructuresonRiemannSurfaces
5.1Preliminaries:CohomologyandHomologyGroups
5.2HarmonicandHolomorphicDifferentialFormsonRiemannSurfaces
5.3ThePeriodsofHolomorphicandMeromorphicDifferentialForms
5.4Divisors.TheRiemann-RochTheorem
5.5Holomorphic1-FormsandMetricsonCompactRiemannSurfaces
5.6DivisorsandLineBundles
5.7ProjectiveEmbeddings
5.8AlgebraicCurves
5.9AbelsTheoremandtheJacobiInversionTheorem
5.10EllipticCurves
Bibliography
IndexofNotation
Index