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bryant r., griffiths p., grossman d. exterior differential systems and euler-lagrange pdes (math.dg_0207039)(draft, 2002)(219s)

bryant r., griffiths p., grossman d. exterior differential systems and euler-lagrange pdes (math.dg_0207039)(draft, 2002)(219s)

ID：14178736

大小：1.33 MB

页数：219页

时间：2018-07-26

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1、ExteriorDi erentialSystemsandEuler-LagrangePartialDi erentialEquationsRobertBryantPhillipGrithsDanielGrossmanJuly3,2002arXiv:math.DG/0207039v13Jul2002iiContentsPrefacevIntroductionvii1LagrangiansandPoincare-CartanForms11.1LagrangiansandContactGeometry................11.2TheEuler-LagrangeSystem...

2、..................71.2.1VariationofaLegendreSubmanifold............71.2.2CalculationoftheEuler-LagrangeSystem.........81.2.3TheInverseProblem.....................101.3Noether'sTheorem..........................141.4HypersurfacesinEuclideanSpace..................211.4.1TheContactManifoldoverEn+1.....

3、.........211.4.2Euclidean-invariantEuler-LagrangeSystems........241.4.3ConservationLawsforMinimalHypersurfaces.......272TheGeometryofPoincare-CartanForms372.1TheEquivalenceProblemforn=2.................392.2Neo-ClassicalPoincare-CartanForms................522.3DigressiononAneGeometryofHypersurfa

4、ces..........582.4TheEquivalenceProblemforn3.................652.5ThePrescribedMeanCurvatureSystem..............743ConformallyInvariantSystems793.1BackgroundMaterialonConformalGeometry...........803.1.1FlatConformalSpace....................803.1.2TheConformalEquivalenceProblem............853.1.3Th

5、eConformalLaplacian..................933.2ConformallyInvariantPoincare-CartanForms.................................973.3TheConformalBranchoftheEquivalenceProblem........102n+23.4ConservationLawsforu=Cun2................1103.4.1TheLieAlgebraofIn nitesimalSymmetries.......1113.4.2CalculationofCons

6、ervationLaws..............114iiiivCONTENTS3.5ConservationLawsforWaveEquations...............1183.5.1EnergyDensity........................1223.5.2TheConformallyInvariantWaveEquation........1233.5.3EnergyinThreeSpaceDimensions.............1274AdditionalTopics1334.1TheSecondVariation..................

7、......1334.1.1AFormulafortheSecondVariation............1334.1.2RelativeConformalGeometry................1364.1.3IntrinsicIntegrationbyParts................1394.1.4PrescribedMeanCurvature,Revisited..........

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