二維球面之間是映射的仲縮度.pdf

1、中國科學技術大學碩士學位論文二維球面之間是映射的仲縮度姓名：曾澤民申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：彭家貴2001.5.1DilatationofmapsbetweentwospheresZegzeminOAbstractLet廠：M—NbeaC’mapoftwoRiemannianmanifoldsandlet諺bethedifferentialoffAsstatedin【1]byprofessorPengjiaguiandT

2、angzi—zhou，indifferentialgeometrywemainlystudytheRiemannianmanifoldsandthemapsbetweenthemAsiswellknown，inasense，thesimplestRiemarmianmanifoldistheunitsphereandthesimplestdifferentiablemapisharmonicmapAnditisalsowellknown

3、thatthesimplestrealalgebraicsetistheunitsphereandthesimplestmapistheentirerationalmapwhichincludespolynomialmapInthisthesis，wemainlydiscussthedilatationofhomogeneouspolynomialmapsbetweentwospheresLetf：S”一S“beaC1mapofthes

4、tandardunitspheresandlet田bethedifferentialoff，F(xiàn)oranypointPonS“，wedefinethedilatationoffatP6。(，)：sup協(xié)(v刪=1’v∈LsljWherellistheEuclideannorrrlFollowingOliver’Sdefinition[21ofthedilatationofthemap：6(，)=sup6，(，)lpcs”Asstatedi

5、n[31，WCdiscusshowtostudythegeometricalcomplexityoffbyitsdilatationIn1998，professorPengjiaguiandTangzizhouprovedin[4】thatlet，：S”_S“beanyhomogeneouspolynomialmapofdegreekbetweenS”andS”，then占(／)≤kAdditionallywhenm=ntheyalso

6、constructthehomogeneouspolynomialmapofdegreekbetweens。andS6：五：S”_∥。where6(^)=kAtthesametime，theyalsoputforwardtheproblemabouttheuniquenessoffwhen占(，)=kForS2，wecanprovethefollowinguniqueresult：Theorem31：Letf：S2_S2beahomog