计算共形几何（英文版）

图书标准信息

• 作者 顾险峰、丘成桐 著
• 出版社 高等教育出版社
• 出版时间 2008-01
• 版次 1
• ISBN 9787040231892
• 定价 49.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 276页
• 字数 340千字

【内容简介】

ThelaunchofthisAdvancedLecturesinMathematicsseriesisaimedatkeepingmathematiciansinformedofthelatestdevelopmentsinmathematics，aswellastoaidinthelearningofnewmathematicaltopicsbystudentsallovertheworld.Eachvolumeconsistsofeitheranexpositorymonographoracollectionofsignifi-cantintroductionstoimportanttopics.Thisseriesemphasizesthehistoryandsourcesofmotivationforthetopicsunderdiscussion,andalsogivesanoverviewofthecurrentstatusofresearchineachparticularfield.Thesevolumesarethefirstsourcetowhichpeoplewillturninordertolearnnewsubjectsandtodis-coverthelatestresultsofmanycutting-edgefieldsinmathematics.

【目录】

Introduction
1.1OverviewofTheories
1.1.1RiemannMapping
1.1.2RiemannUniformization
1.1.3ShapeSpace
1.1.4GeneralGeometricStructure
1.2AlgorithmsforComputingConformalMappings
1.3Applications
1.3.1ComputerGraphics
1.3.2ComputerVision
1.3.3GeometricModeling
1.3.4MedicalImaging
FurtherReadings

PartITheories
2HomotopyGroup
2.1AlgebraicTopologicalMethodology
2.2SurfaceTopologicalClassification
2.3HomotopyofContinuousMappings
2.4HomotopyGroup
2.5HomotopyInvariant
2.6CoveringSpaces
2.7GroupRepresentation
2.8Seifert-vanKampenTheorem
Problems
3HomologyandCohomology
3.1SimplicialHomology
3.1.1SimplicialComplex
3.1.2GeometricApproximationAccuracy
3.1.3ChainComplex
3.1.4ChainMapandInducedHomomorphism
3.1.5SimplicialMap
3.1.6ChainHomotopy
3.1.7HomotopyEquivalence
3.1.8RelationBetweenHomologyGroupandHomotopyGrou
3.1.9LefschetzFixedPoint
3.1.10Mayer-VietorisHomologySequence
3.1.11TunnelLoopandHandleLoop
3.2Cohomology
3.2.1CohomologyGroup
3.2.2CochainMap
3.2.3CochainHomotopy
Problems
4ExteriorDifferentialCalculus
4.1SmoothManifold
4.2DifferentialForms
4.3Integration
4.4ExteriorDerivativeandStokesTheorem
4.5DeRhamCohomologyGroup
4.6HarmonicForms
4.7HodgeTheorem
Problems
5DifferentialGeometryofSurfaces
5.1CurveTheory
5.2LocalTheoryofSurfaces
5.2.1RegularSurface
5.2.2FirstFundamentalForm
5.2.3SecondFundamentalForm
5.2.4WeingartenTransformation
5.3OrthonormalMovableFrame
5.3.1StructureEquation
5.4CovariantDifferentiation
5.4.1GeodesicCurvature
5.5Gauss-BonnetTheorem
5.6IndexTheoremofTangentVectorField
5.7MinimalSurface
5.7.1WeierstrassRepresentation
5.7.2CostaMinimalSurface
Problems
6RiemannSurface
6.1RiemannSurface
6.2RiemannMappingTheorem
6.2.1ConformalModule
6.2.2Quasi-ConformalMapping
6.2.3HolomorphicMappings
6.3HolomorphicOne-Forms
6.4PeriodMatrix
6.5Riemann-RochTheorem
6.6AbelTheorem
6.7Uniformization
6.8HyperbolicRiemannSurface
6.9TeichmiillerSpace
6.9.1Quasi-ConformalMap
6.9.2ExtremalQuasi-ConformalMap
6.10Teichm011erSpaceandModularSpace
6.10.1FrickeSpaceModel
6.10.2GeodesicSpectrum
Problems
……

PartIIAlgorithms
AMajorAlgorithms
BAcknowledgement
Reference
Index