几何测度论

图书标准信息

• 作者 [美]摩根 著
• 出版社 世界图书出版公司
• 出版时间 2009-05
• 版次 1
• ISBN 9787506292085
• 定价 39.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 248页
• 正文语种 英语
• 原版书名 Geometric Measure Theory

【内容简介】

　　Singulargeometrygovernsthephysicaluniverse：soapbubbleclustersmeetingalongsingularcurves，blackholes，defectsinmaterials，chaoticturbulence，crys-talgrowth.Thegoverningprincipleisoftensomekindofenergyminimization.Geometricmeasuretheoryprovidesageneralframeworkforunderstandingsuchminimalshapes，aprioriallowinganyimaginablesingularityandthenprovingthatonlycertainkindsofstructuresoccur.

【目录】

Prefacevii
1GeometricMeasureTheory
2Measures
3LipschitzFunctionsandRectifiableSets
4NormalandRectifiableCurrents
5TheCompactnessTheoremandtheExistenceofArea-MinimizingSurfaces
6ExamplesofArea-MinimizingSurfaces
7TheApproximationTheorem
8SurveyofRegularityResults
9MonotonicityandOrientedTangentCones
10TheRegularityofArea-MinimizingHypersurfaces
11FlatChainsModulov，Varifolds，andMinimalSets
12MiscellaneousUsefulResults
13SoapBubbleClusters
14ProofofDoubleBubbleConjecture
15TheHexagonalHoneycombandKelvinConjectures
16ImmiscibleFluidsandCrystals
17IsoperimetricTheoremsinGeneralCodimension
18ManifoldswithDensityandPerelmansProofofthePoincareConjecture
19DoubleBubblesinSpheres，GaussSpace，andTori
SolutionstoExercises
Bibliography
IndexofSymbols
NameIndex
SuhiectIndex