课程简介：Inthiscoursewe\'llpresentbasicmaterialsonEinsteinmanifoldsandRicciflow,includingpartofHamilton\'stheoryoftheRicciflowandpartofPerelman\'stheoryoftheRicciflow,suchasthevariationaltheoryofEinsteinmetrics,obstructiontoexistenceofEinsteinmetrics,short-timeexistenceoftheRicciflow,2-dimensionalRicciflow,3-dimensionalRicciflow,blow-upsingularities,theentropyfunctional,non-collapsingoftheRicciflow,themaximumprinciplesandtheHarnackinequalities.ThetheoryofEinsteinmanifoldsandthetheoryoftheRicciflowhavehadmajoradvancesinrecentyears,includingPerelman\'ssolutionofthePoincareconjectureusingtheRicciflow.Thiscourseismeanttoprovidefoundationalknowledgeandskillsforunderstandingmoreadvancedworkinthesefields.

Inthiscoursewe\'llpresentbasicmaterialsonEinsteinmanifoldsandRicciflow,includingpartofHamilton\'stheoryoftheRicciflowandpartofPerelman\'stheoryoftheRicciflow,suchasthevariationaltheoryofEinsteinmetrics,obstructiontoexistenceofEinsteinmetrics,short-timeexistenceoftheRicciflow,2-dimensionalRicciflow,3-dimensionalRicciflow,blow-upsingularities,theentropyfunctional,non-collapsingoftheRicciflow,themaximumprinciplesandtheHarnackinequalities.ThetheoryofEinsteinmanifoldsandthetheoryoftheRicciflowhavehadmajoradvancesinrecentyears,includingPerelman\'ssolutionofthePoincareconjectureusingtheRicciflow.Thiscourseismeanttoprovidefoundationalknowledgeandskillsforunderstandingmoreadvancedworkinthesefields.