空間形式中的極小子流形及常均曲率超曲面.pdf

1、中國(guó)科學(xué)技術(shù)大學(xué)博士學(xué)位論文空間形式中的極小子流形及常均曲率超曲面姓名：許志才申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：徐森林2001.10.1●AbstractTmspapcrstIldiesm“血alsubm越foldsandhypersu血ceswi血cons眥meancurvanlr℃訪spaceformsFirsⅡyweconsiderthecornpactminirnalsubmaIlifoldsi11meunitspher

2、cs斛9Afbercalculatingandest蚰atingmeL印lacianoftheenergyden8時(shí)ofGaussm印，we垂vea‘Pinching”也eorem塒lichinvolvestheRjccicllⅣa：七Ilreandthesquareoft11elen甜hofmesecond丘md暑Lmentalfonn，mereforeimproves出ePaIl’sresultSecondly，weconsider

3、也espacel岫ro詛tionalWhypersu如esiIlLorentz，Mi士lkowsHspace鐘，obtaitlmedi臟rentialequationsof婦gene瑚咖gcurvesof恤sehypersllrfaces，andgive也eroIIingcons仃l州onof血esehypersul白cesTllisdemonstrates也atitisalwayspossibletousemerollingcon蚶u

4、ctiont0‰formmeproblcmofsolVmg也eequatioIlsofgeneratingcuⅣest0也eproblemofsolVingtlleequatbnSofcorrcspondingcurves，whichisageneralizationofDelaunay’sr01lingcons咖cti曲in3dilnensionalEuclideanspaceThirdlywecotlsider也ehyperslld

5、沁es誦thconstantmeancuⅣ柵e址deSitterspaceAnextrari西di諺theoremandtwoi衄erri酉di母theoremsaredbtainedTheset王IeoremsaIlswerp刪y也eGodda匝寸sco面ecnlre，iecompletespaceIikehypersurfaceIvitllconstantmeancuⅣaturemustbeⅧ曲ilicalWealso百ve柚exi

6、stencetheoremofspacelikero協(xié)tionalWhypersurfaceindeSit【erspaceFinallywecons試crmeisopara玎1e越chypersu血ceincomplexhyperbolicspaceWhenn2，weobtaintvmt11eorems，oneweakenst11econditionofBemdrscl船sifkationtheorem，也eo血ersolvesmevI