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[美] 摩根 著 / 世界图书出版公司 / 2009-05 / 平装
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几何测度论
Singulargeometrygovernsthephysicaluniverse:soapbubbleclustersmeetingalongsingularcurves,blackholes,defectsinmaterials,chaoticturbulence,crys-talgrowth.Thegoverningprincipleisoftensomekindofenergyminimization.Geometricmeasuretheoryprovidesageneralframeworkforunderstandingsuchminimalshapes,aprioriallowinganyimaginablesingularityandthenprovingthatonlycertainkindsofstructuresoccur.
Prefacevii1GeometricMeasureTheory2Measures3LipschitzFunctionsandRectifiableSets4NormalandRectifiableCurrents5TheCompactnessTheoremandtheExistenceofArea-MinimizingSurfaces6ExamplesofArea-MinimizingSurfaces7TheApproximationTheorem8SurveyofRegularityResults9MonotonicityandOrientedTangentCones10TheRegularityofArea-MinimizingHypersurfaces11FlatChainsModulov,Varifolds,andMinimalSets12MiscellaneousUsefulResults13SoapBubbleClusters14ProofofDoubleBubbleConjecture15TheHexagonalHoneycombandKelvinConjectures16ImmiscibleFluidsandCrystals17IsoperimetricTheoremsinGeneralCodimension18ManifoldswithDensityandPerelmansProofofthePoincareConjecture19DoubleBubblesinSpheres,GaussSpace,andToriSolutionstoExercisesBibliographyIndexofSymbolsNameIndexSuhiectIndex
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