几何分析手册（第Ⅰ卷）（英文）

GeometricAnalysiscombinesdifferentialequationsanddifferentialgeometry.Animportantaspectistosolvegeometricproblemsbystudyingdifferentialequations.BesidessomeknownlineardifferentialoperatorssuchastheLaplaceoperator，manydifferentialequationsarisingfromdifferentialgeometryarenonlinear.AparticularlyimportantexampleistheMonge-Ampereequation.Applicationstogeometricproblemshavealsomotivatednewmethodsandtechniquesindifferen-tialequations.Thefieldofgeometricanalysisisbroadandhashadmanystrikingapplications.Thishandbookofgeometricanalysisprovidesintroductionstoandsurveysofimportanttopicsingeometricanalysisandtheirapplicationstorelatedfieldswhichisintendtobereferredbygraduatestudentsandresearchersinrelatedareas.