| 摘要 | 第1-6页 |
| Preface | 第6-16页 |
| Abstract | 第16-29页 |
| Chapter 0 Preliminaries | 第29-38页 |
| 0．1 Notations and Local Formulae | 第29-32页 |
| 0．2 Some Properties of Eigenvalues and Heat Kernel | 第32-36页 |
| 0．3 Some Useful Lemmas | 第36-38页 |
| Chapter 1 Global Pinching Theorems for Submanifolds | 第38-69页 |
| 1．1 Main Results | 第39-43页 |
| 1．2 Geometric Inequalities for Submanifolds with PMC | 第43-54页 |
| 1．3 Pinching Theorem for Submanifolds in a Pinched Riemannian Maniflold | 第54-65页 |
| 1．4 Geometric Inequalities for Minimal Submanifolds | 第65-67页 |
| 1．5 Pinching Theorem for Submanifl01ds in a Pinched Locally Symmetric Riematinian Manifold | 第67-69页 |
| Chapter 2 Rigidity for Complete Submanifolds with PMC | 第69-87页 |
| 2．1 Main Results | 第69-73页 |
| 2．2 Maximal Direction and Lower Bound of Ricci Curvature for Submanifolds | 第73-80页 |
| 2．3 Rigidity for Complete Submanifolds with PMC | 第80-87页 |
| Chapter 3 Topological Sphere Theorems for Submanifolds | 第87-99页 |
| 3．1 Main Results | 第87-90页 |
| 3．2 Topological Sphere Theorem for Submanifolds in a Sphere | 第90-95页 |
| 3．3 Topological Sphere Theorem for Submanifolds in a Pinched Riemannian Manifold | 第95-99页 |
| Chapter 4 Geometric Lower Bounds for Eigenvalues of Submanifolds | 第99-109页 |
| 4．1 Main Results | 第99-103页 |
| 4．2 Lower Bound for First Eigenvalue | 第103页 |
| 4．3 Geometric Lower Bound for Higher Eigenvalues | 第103-109页 |
| Bibliography | 第109-116页 |
| Curriculum Vitae | 第116-117页 |
| Acknowledgements | 第117页 |
