简介：Inthispaper,weinvestigateahorizontalLaplacianversionoftheclampedplateproblemonCarnotgroupsandobtainsomeuniversalinequalities.Furthermore,forthelowerordereigenvaluesofthiseigenvalueproblemoncarnotgroups,wealsogivesomeuniversalinequalities.

简介：ForaCarnotgroupG,weestablishtherelationshipbetweenextendedmeanvaluesandr-convexfunctionswhichisintroducedinthispaper,whichisaclassofinequalitiesofHadamardtypeforr-convexfunctiononG.

简介：Thispaperstudiesthepropertiesofsolutionsofquasilinearequationsinvolvingthep-laplaciantypeoperatoringeneralCarnot-Carath6odoryspaces.Theauthorsshowsomecom-parisonresultsforsolutionsoftherelevantdifferentialinequalitiesandusethemtogetsomesymmetryandmonotonicitypropertiesofsolutions,inboundedorunboundeddomains.

简介：polarizableCarnot组的一些新性质被给。由在thepolarizableCarnot上选一个合适的常数为非分叉Dirichlet问题的一个班的一个重要答案，组被构造。因此，correspondingnon同类的Dirichlet问题的多答案性质被证明，在famousAlexandrov-Bakelman-Pucci类型估计的L~Q标准可能的最好被讨论。