| 摘要 | 第7-8页 |
| Abstract | 第8页 |
| Preliminaries | 第10-16页 |
| 0.1 The introduction of convex geometric analysis | 第10-14页 |
| 0.2 Main results of this dissertation | 第14-16页 |
| 1 Quasi L_p Busemann-Petty inequalities for L_p mixed intersection body | 第16-28页 |
| 1.1 Introduction | 第16-18页 |
| 1.2 Basic defnition and notation | 第18-21页 |
| 1.3 The analog L_p Busemann-Petty intersection inequality of L_p mixed intersection body and its star dual body | 第21-25页 |
| 1.4 The analog L_p Busemann-Petty intersection inequality of L_p mixed intersection body of star dual body | 第25-28页 |
| 2 λ-intersection bodies and an analytic generalized Busemann-Petty problem | 第28-44页 |
| 2.1 Introduction | 第28-34页 |
| 2.2 Notation and Preliminaries | 第34-37页 |
| 2.3 Proofs of our main results | 第37-44页 |
| 3 Two complex combinations and complex intersection bodies | 第44-68页 |
| 3.1 Introduction | 第44-49页 |
| 3.2 Preliminaries | 第49-52页 |
| 3.3 Dual mixed volume for complex combinations | 第52-58页 |
| 3.4 Complex radial Blaschke linear combination for com-plex intersection bodies | 第58-63页 |
| 3.5 Geometric inequalities | 第63-68页 |
| Further Research | 第68-70页 |
| References | 第70-78页 |
| Completed Papers During Graduate Study Period | 第78-80页 |
| Acknowledgements | 第80-82页 |
| 致谢 | 第82页 |
