Some Properties Of Compact Minimal Hypersurface

In this thesis, some properties of compact minimal hypersurface areinvestigated and analyzed in four chapters.In chapterⅠ, the history of diferential geometry is overviewed. Thenthe task and contributions of this thesis are presented.In chapterⅡ, some related concepts and important lemmas of difer-ential geometry are introduced as the basis of our work.In chapterⅢ, the basic equations of isometric immersed submanifoldare discussed.In the last chapter, the properties of compact minimal hypersurfaceare studied. Firstly, the equivalent conditions of the important theoremwhich was described in the literature are derived and its conclusions arepromoted. Secondly, the compact minimal hypersurface in the quasi con-stant curvature space is invertigated. Finally, some new conclusions areobtained from the compact minimal hypersurface when the value of con-stant sectional curvature equals to one.