| 1 An analogue of the Euler formula | 第1-17页 |
| ·Introduction and basic concepts | 第12-14页 |
| ·preliminary | 第14-15页 |
| ·prove the conclusion | 第15-17页 |
| 2 The bonnesen-type inequality on constant plane | 第17-30页 |
| ·Basic concepts of convex sets in Euclidean space | 第18-20页 |
| ·Basic concepts of convex sets and convex curves | 第18页 |
| ·Support lines and their existence | 第18-20页 |
| ·Measure for sets and formulas of integral geometry | 第20-25页 |
| ·Measure for sets of geometric elements | 第20-22页 |
| measure for sets of points | 第20-21页 |
| Measure for sets of lines | 第21-22页 |
| ·Formulas of integral geometry in the plane | 第22-25页 |
| The group of motion | 第22-23页 |
| The differential form on G | 第23-24页 |
| The kinematic density | 第24-25页 |
| Poincare's formula and Blaschke formula | 第25页 |
| ·Isoperimetric inequality | 第25-30页 |
| ·Isoperimetric inequality | 第25-26页 |
| ·stronger isoperimetric inequalities | 第26-28页 |
| ·An upper limit for isoperimetric deficit | 第28-30页 |
| 3 conclusions | 第30-40页 |
| ·Bonnesen-type inequality in non-Euclidean plane | 第30-37页 |
| ·some preliminaries and concepts | 第30-32页 |
| ·Bonnesen-type inequalitise in the hyperbolic plane H~2 | 第32-35页 |
| ·Bonnesen-type inequalities in projective plane PR~2 | 第35-37页 |
| ·An upper limit in constant plane | 第37-40页 |
| ·the kinematic formula in constant plane | 第37-38页 |
| ·An upper limits in non-Euclidean plane | 第38-40页 |
| An upper limits in hyperbolic plane | 第38-39页 |
| An upper limits in projective plane | 第39-40页 |
| Bibliography | 第40-43页 |
| 原创性声明 | 第43页 |
| 关于学位论文使用授权的声明 | 第43页 |
