中国科大学位与研究生教育
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主讲教师:DE PAUW Thierry 人气:354 更新时间: 2018年03月03日
Abstract:IfXisasmoothcompactRiemannianmanifoldtheneachhomologyclasswithintegercoefficientsadmitsamassminimizingintegralcurrentrepresentative.Thisresult,duetoH.FedererandW.H.Fleming,reliesoncompactnessandtheisoperimetricinequality.InthistalkIextendthisresulttoaclassofsingularspacesX.Theseincludesemialgebraicsets,subanalyticsets,andmoregenerallysetsdefinableinanyo-minimalstructure.SimpleexamplesofcuspsshowthattheEuclideanisoperimetricinequalitydoesnotholdinthisgeneralityandwemustsettleforaweakerversion.Thisleadstodevelopingatheoryoffunctionsofboundedvariationdefinedonintegralcurrents.
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