几何分析手册（第Ⅰ卷）（英文）

图书标准信息

• 作者 季理真 编
• 出版社 高等教育出版社
• 出版时间 2008-08
• 版次 1
• ISBN 9787040252880
• 定价 128.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 676页
• 字数 820千字
• 正文语种 英语

【内容简介】

GeometricAnalysiscombinesdifferentialequationsanddifferentialgeometry.Animportantaspectistosolvegeometricproblemsbystudyingdifferentialequations.BesidessomeknownlineardifferentialoperatorssuchastheLaplaceoperator，manydifferentialequationsarisingfromdifferentialgeometryarenonlinear.AparticularlyimportantexampleistheMonge-Ampereequation.Applicationstogeometricproblemshavealsomotivatednewmethodsandtechniquesindifferen-tialequations.Thefieldofgeometricanalysisisbroadandhashadmanystrikingapplications.Thishandbookofgeometricanalysisprovidesintroductionstoandsurveysofimportanttopicsingeometricanalysisandtheirapplicationstorelatedfieldswhichisintendtobereferredbygraduatestudentsandresearchersinrelatedareas.

【目录】

NumericalApproximationstoExtremalMetricsonToricSurfaces
1Introduction
2Theset-up
2.1Algebraicmetrics
2.2Decompositionofthecurvaturetensor
2.3Integration
3Numericalalgorithms：balancedmetricsandrefinedapproximations
4Numericalresults
4.1Thehexagon
4.2Thepentagon
4.3Theoctagon
4.4Theheptagon
5Conclusions
References

KahlerGeometryonToricManifolds,andsomeotherManifoldswithLargeSymmetry
Introduction
1Background
1.1Gaugetheoryandholomorphicbundles
1.2Symplecticandcomplexstructures
1.3Theequations
2Toricmanifolds
2.1Localdifferentialgeometry
2.2Theglobalstructure
2.3Algebraicmetricsandasymptotics
2.4Extremalmetricsontoricvarieties
3ToricFanomanifolds
3.1TheKahler-Riccisolitonequation
3.2Continuitymethod,convexityandafundamentalinequality
3.3Aprioriestimate
3.4ThemethodofWangandZhu
4Variantsoftoricdifferentialgeometry
4.1Multiplicity-freemanifolds
4.2Manifoldswithadenseorbit
5TheMukai-Umemuramanifoldanditsdeformations
5.1Mukai'sconstruction
5.2Topologicalandsymplecticpicture
5.3Deformations
5.4Thea-invariant
References

GluingConstructionsofSpecialLagrangianCones
1Introduction
2SpecialLagrangianconesandspecialLegendriansubmanifoldsofS2n-1
3CohomogeneityonespecialLegendriansubmanifoldsofS2n-1
4ConstructionoftheinitialalmostspecialLegendriansubmanifolds
5Thesymmetrygroupandthegeneralframeworkforcorrectingtheinitialsurfaces
6Thelinearizedequation
7UsingtheGeometricPrincipletoprescribetheextendedsubstitutekernel
8Themainresults
ASymmetriesandquadratics
References

HarmonicMappings
1Introduction
2HarmonicmappingsfromtheperspectiveofRiemanniangeometry
2.1HarmonicmappingsbetweenRiemannianmanifolds：definitionsandproperties
2.2Theheatflowandharmonicmappingsintononpositivelycurvedmanifolds
2.3HarmonicmappingsintoconvexregionsandapplicationstotheBernsteinproblem
3Harmonicmappingsfromtheperspectiveofabstractanalysisandconvexitytheory
3.1Existence
3.2Regularity
3.3Uniquenessandsomeapplications
4HarmonicmappingsinKahlerandalgebraicgeometry
4.1Rigidityandsuperrigidity
4.2Harmonicmapsandgrouprepresentations
4.3Kahlergroups
4.4Quasiprojectivevarietiesandharmonicmappingsofinfiniteenergy
5HarmonicmappingsandRiemannsurfaces
5.1FamiliesofRiemannsurfaces
……
HarmonicFunctionsonCompleteRiemannianManifolds
ComplexityofSolutionsofPartialDifferentialEquations
VariationalPrinciplesonTriangulatedSurfaces
AsymptoticStructuresintheGeometryofStabilityandExtremalMetrics
StableConstantMeanCurvatureSurfaces
AGeneralAsymptoticDecayLemmaforEllipticProblems
UniformizationofOpenNonnegativelyCurvedK／ihlerManifoldsinHigherDimensions
GeometryofMeasures：HarmonicAnalysisMeetsGeometricMeasureTheory
TheMongeAmpereEequationanditsGeometricAapplications
LecturesonMeanCurvatureFlowsinHigherCodimensions
LocalandGlobalAnalysisofEigenfunctionsonRiemannianManifolds
Yau’SFormofSchwarzLemmaandArakelovInequalityOnModuliSpacesofProjectiveManifolds