中国科学技术大学硕士学位论文庞加莱猜想证明的概述姓名：官永辉申请学位级别：硕士专业：基础数学指导教师：@2011-05Á‡©Ì‡ùãÁ²§ù~ÀXÛ^Hamilton-PerelmanRicci65y²\4ߎ"ÏLOŽÝþuЕ§±9?1DeTurckC†§Œ±y²Ricci6)ážm•35"ÏLRicci6•§ÚOŽC†Œ±•ÇuЕ§§lŒ±y²•Ç÷vShiFÝO"½ÂMα╆•Çƒ'þ§ÏL•ÇuЕ§MαβuЕ§§MαβuЕ§÷vHamilton4ŒŠn¤I^‡§lMαβ÷vHamilton4ŒŠn",§ÏL|^•ÇuЕ§ÚLi-Yau-Hamilton/ª§Œ±êþ•ÇLi-Yau-Hamiltonت"•y²šÛÜ¥½n§PerelmanÚ?L-•ÝÚPerelmanzNÈVg§ÏLPerelmanzNÈüN5y²šÛÜ¥½n"dšÛÜ¥½nŒ±‰Ñ•ÇÛÜSŒ»O§=kLittleLoopÚn"•IPuÐ6/S4•§Hamiltony²Hamilton;5½n§Hamilton;5½n‡¦IP6/Säk˜—SŒ»e.§šÛÜ¥½néÐ)ûù‡¯K"Hamilton;5½néuy²¥½nÚ;‰•½n镇"d§Hamilton„•Ricci6)ïáÛÉ(§ò4Œ)©•na§z˜akƒAÛÉ.§¿éz˜aÛÉ.5Ÿ?1©Û"Hamiltony²n‘¥½n§‰Ñn‘;—šKRicci•Ç6/("éuRicci•Ç6/5`§§‡©ÓuS3½§û˜m"d§n‘6/Ricci6÷vPinchingO§PinchingOL²n‘4•)7½kšK•ÇŽf"éun‘ancientκ-)§˜•¡§PerelmanwŠ·‚§§kéÐý.O§FÝOÚ;‰•½n";‰•½nL²§éun‘ancientκ-)§ž˜6/z˜:Ñk±enam•ƒ˜§ùnam•©O´¥G§¶G½lG",˜•¡§Perelman‰ÑRicci6ÛÉ(§3•Ç錞˜:§kaqancientκ-)(Úaq5Ÿ§'XFÝO§;‰•½n§lÛÉ)•k;‰•½n"kc¡O§e5ò´©Ì‡ù)Ü©"éun‘;—Œ½•6/§Á²§ù~À‰ÑéRicci6?1ÃâäNÚ½§Ì‡•¹äÃâÚ¿K,;©|"?˜Ú§‡ÀÜ·äÃâÚ;‰•Œ»§¦)Ø=÷vPinchingbÚ;‰•b§…3k•žm•‰k•gÃâ"•ª§òPerelmanJÑÃâzRicci6)•žm•35½n"éun‘;—üëÏ6/§Colding-Minicozik•ž”½nL²)3k•žmž”§ldþã•žm•35½n±96/üëÏ5§6/‡©Óiiun‘¥¡"'…iµRicci6§\4ߎFÝO§ÛÜ¥½n§Hamilton;5½n§n‘¥½n§Ãâ§Pinchingb§;‰•½n§•žm•35½n"iiiAbstractInthisthesis,wemainlydiscusshowHuaidongCaoandXipingZhuusethemethodofRicciflowtoprovePoincar´econjecture.Wecangettheshort-timeexistenceofthetoRicciFlowbycomputingtheevovlingequationofthemetricandDeTurckchange.Wecangettheevovlingequationofcurvaturebycomputing,andhencewecangetthederivativeestimateofcurvatureofShi.TheevovlingequationofthedefinedMαβwhichisrelevanttocurvaturesatisfiestheconditonofHamilton'sStrongMaximumPrinciple,soMαβsatisfiesHamilton'sStrongMaximumPrinciple.Futhermore,thescalarcurvaturealsosatisfiestheLi-Yau-Hamiltoninequality.Inordertoprovethenolocalcollapsingtheorem,Perelmanus