| 1 Introduction | 第9-15页 |
| 2 Main notions | 第15-36页 |
| 2.1 Carnot-Caratheodory spaces | 第15-18页 |
| 2.2 Carnot groups | 第18-27页 |
| 2.2.1 Carnot groups of step two | 第22-25页 |
| 2.2.2 Groups of Heisenberg type | 第25-27页 |
| 2.3 Some general results in Carnot groups | 第27-29页 |
| 2.4 Convex functions on Carnot groups | 第29-36页 |
| 2.4.1 Definition of convex functions | 第29-33页 |
| 2.4.2 Basic properties of convex functions | 第33-36页 |
| 3 Inequalities of Hadamard Type for r-Convex Functions | 第36-55页 |
| 3.1 Introduction | 第36-37页 |
| 3.2 Definitions and main results | 第37-43页 |
| 3.3 Basic properties for r-convex functions | 第43-46页 |
| 3.4 The proofs of theorems | 第46-51页 |
| 3.5 Some simple applications | 第51-55页 |
| 4 Lipschitz continuity of H-convex functions | 第55-70页 |
| 4.1 A new proof of Lipschitz continuity of H-convex functions in H" | 第56-61页 |
| 4.2 A characterization of H-convex functions | 第61-66页 |
| 4.3 Lipschitz continuity of H-convex functions in Carnot groups | 第66-70页 |
| 5 Comparison principle of convex functions | 第70-93页 |
| 5.1 Introduction | 第70-76页 |
| 5.2 Comparison principle | 第76-84页 |
| 5.3 Applications | 第84-93页 |
| 6 H-quasiconvex functions | 第93-109页 |
| 6.1 Definitions and some basic properties | 第93-95页 |
| 6.2 H-quasiconvpx functions coincide with H-convex level sets | 第95页 |
| 6.3 A characterization | 第95-97页 |
| 6.4 Estimates of the L~∞ norm of first derivative | 第97-100页 |
| 6.5 Boundedness from above | 第100-109页 |
