一致Cantor集的Minkowski容度.pdf

1、華中師范大學(xué)碩士學(xué)位論文一致Cant集的Minkowski容度姓名：蔣鋒申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：陳世榮20050501⑩碩士學(xué)位論文MASTER’STHESISAbstractNOWsomegoodresultshavebeenobtalnedfortheMinkowskidimensionofsomesetsinanButsomeresultsoftheMinkowskicontentsofthesetsarenot

2、veryperfectTheMinkowskicontentsofthesetsmaybeinfiniteorfinite(possiblyzero)，whichisconcernedbymanyscholars，EspeciallyLapidustransformedtheproblemofestimatingeigenvaluenumbersoftheLaplace’Sequationintotheproblemofcalculat

3、ingtheMinkowskicontentonthefractMboundaries，whenhestudiedtheWeyl—BerryconjectureofthefractaldrumItisveryimportanttostudytheMinkowskicontentsofsonicsets，especiallyfortheresearchoftheWeylBerryconjectureLapidushadprovedtheM

4、inkowskimeasurabilityofsomecompactsubsetsinRandprovedtheModified～VeylBerryCOnjectureinthecasen=1Moreover，heestablished，intheprocess，someunexpectedandintriguingconnectionsbetweenspectralgeometry，fractalgeometryandtheRiema

5、nnzetafunctionAtthesametimethisisincontrastto7’exceptional”caseswhichhappentoincludetheusualmiddlethirdCan—totsetshownbyLapidusandPomerancenottobeMinkowskimeasurableAssociateProfessorShirongCheninCCNUalsostudiedthecounta

6、blesetsintheintervalf0，1]andobtainitsMinkowskicontentanddimension，InthepaperwestudytheuniformCantorsetsWefirstlygivesomepropertiesofMinkowskicontentandcalculateitsHausdorffmeasureandupPerandlowerMinkowskic。ntentsThatis，M

7、(D，F(xiàn))2麗re[云(1看C]薩萬和尬(D，F(xiàn))=古(考％)1。DThusweeasilyobtainthattheMinkowskicontentoftheuniformCantorsetsdoesnotexistThereforeweobtainthatitisnotMinkowskimeasurablebyanewmethodKeywords：Minkowskimeasurable；UniformCantorset；Minkow