convex geometric analysis

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1、ConvexGeometricAnalysisMSRIPublicationsVolume34,1998ContentsIntroduction:TheConvexGeometryandGeometricAnalysisProgram,MSRI,Spring1996ixProgramSeminarsxiGAFASeminars1994–1996xixIntegralsofSmoothandAnalyticFunctionsoverMinkowski’sSumsofConvexSets1SemyonAlesker

2、LocalizationTechniqueontheSphereandtheGromov–MilmanTheoremontheConcentrationPhenomenononUniformlyConvexSphere17SemyonAleskerGeometricInequalitiesinOptionPricing29ChristerBorellRandomPointsinIsotropicConvexSets53JeanBourgainThresholdIntervalsunderGroupSymmetr

3、ies59JeanBourgainandGilKalaiOnaGeneralizationoftheBusemann–PettyProblem65JeanBourgainandGaoyongZhangIsotropicConstantsofSchattenClassSpaces77SeanDarOntheStabilityoftheVolumeRadius81EfimD.GluskinPolytopeApproximationsoftheUnitBallof`n89pW.TimothyGowersARemark

4、abouttheScalar-Plus-CompactProblem111W.TimothyGowersviiviiiCONTENTSAnotherLow-TechnologyEstimateinConvexGeometry117GregKuperbergOntheEquivalenceBetweenGeometricandArithmeticMeansforLog-ConcaveMeasures123RafalLatalaOntheConstantintheReverseBrunn–MinkowskiIneq

5、ualityforp-ConvexBalls129AlexanderE.LitvakTheExtensionoftheFinite-DimensionalVersionofKrivine’sTheoremtoQuasi-NormedSpaces139AlexanderE.LitvakANoteonGowers’DichotomyTheorem149BernardMaureyAn“Isomorphic”VersionofDvoretzky’sTheorem,II159VitaliMilmanandGideonSc

6、hechtmanAsymptoticVersionsofOperatorsandOperatorIdeals165VitaliMilmanandRoyWagnerMetricEntropyoftheGrassmannManifold181AlainPajorCurvatureofNonlocalMarkovGenerators189MichaelSchmuckenschlager•AnExtremalPropertyoftheRegularSimplex199MichaelSchmuckenschlager•F

7、loatingBody,IlluminationBody,andPolytopalApproximation203CarstenSchutt•ANoteontheM¤-LimitingConvolutionBody231AntonisTsolomitisConvexGeometricAnalysisMSRIPublicationsVolume34,1998IntegralsofSmoothandAnalyticFunctionsoverMinkowski’sSumsofConvexSetsSEMYONALESK

8、ER1.IntroductionandStatementofMainResultsLetK¯=(K;K;:::;K)beans-tupleofcompactconvexsubsetsofRn.12sForanycontinuousfunctionF:Rn¡!C,considerthefunctionMssK¯F:R+¡!C;whereR+=f(¸1;:::;¸s)j¸j¸0g;defin