| 摘要 | 第1-9页 |
| Abstract | 第9-11页 |
| 1 Introduction and preliminaries | 第11-20页 |
| ·Basic concepts of convex sets in R~n | 第11-12页 |
| ·Convex body and convex surface | 第11-12页 |
| ·Support hyperplane and their existence | 第12页 |
| ·Quermassintegrale and integrals of mean curvature | 第12-16页 |
| ·Quermassintegrale | 第12-13页 |
| ·Integrals of mean curvature | 第13-15页 |
| ·Relations between integrals of mean curvature and quer-massintegrale | 第15页 |
| ·Santalò's formula | 第15-16页 |
| ·Geometry measure and kinematic fundamental formulas | 第16-18页 |
| ·Measure for sets of geometric elements | 第16-17页 |
| ·Kinematic fundamental formulas | 第17-18页 |
| ·Isoperimetric inequality | 第18-20页 |
| ·Classical isoperimetric inequality | 第18页 |
| ·Stronger isoperimetric inequalities | 第18-20页 |
| 2 Bonnesen-type inequalities in the Euclidean space R~3 | 第20-26页 |
| ·Containment measure of one convex body to contain another in R~3 | 第20-22页 |
| ·Some preliminaries and concepts | 第20-22页 |
| ·Containment measure for one convex body to contain another in R~3 | 第22页 |
| ·Bonnesen-type inequalities about convex body in R~3 | 第22-26页 |
| 3 Bonnesen-type inequalities in the Euclidean space R~4 | 第26-30页 |
| ·Containment measure of one convex body to contain another in R~4 | 第26-27页 |
| ·Bonnesen-type inequalities about convex body in R~4 | 第27-30页 |
| 4 Bonnesen-type inequalities in the Euclidean space R~n | 第30-35页 |
| ·Containment measure of one convex body to contain another in R~n | 第30-31页 |
| ·Bonnesen-type inequalities about convex body in R~n | 第31-35页 |
| Bibliography | 第35-37页 |
| Acknowlegements | 第37-38页 |
