| Chapter 0 Introduction | 第1-11页 |
| Chapter 1 The Heisenberg group and the maps for the group targets | 第11-25页 |
| ·The construction of the Heisenberg group H~n | 第11-18页 |
| ·The basic properties of the Heisenberg group (H~n, d) | 第18-23页 |
| ·The Lipschitz maps for the Heisenberg group targets | 第23-25页 |
| Chapter 2 L~p(Ω,H~n), W~(1,p)(Ω, H~n) and BMO(Ω,H~n) | 第25-51页 |
| ·Definition and basic properties of L~p(Ω, H~n) | 第25-34页 |
| ·Definition and basic properties of W~(1,p)(Ω, H~n) | 第34-38页 |
| ·Pre-norm and Pre-weakly compactness on W~(1,p)(Ω, H~n) | 第38-43页 |
| ·BMO spaces and John-Nirenberg estimates for the Heisenberg group targets | 第43-51页 |
| Chapter 3 Poincaré inequalities and reverse Poincaré inequalities in W~(1,p)(Ω, H~n) | 第51-67页 |
| ·The Poincaré inequalities | 第51-55页 |
| ·The reverse Poincaré inequality about Legendrian energy minimizers for Heisenberg group targets | 第55-67页 |
| Chapter 4 The Hlder continuities of the maps in W~(1,p)(Ω, H~n) and embedding theorems | 第67-82页 |
| Chapter 5 The existence and the Euler equations of the minimizers in W~(1,p)(Ω, H~n) | 第82-92页 |
| ·The existence of the minimizers | 第82-85页 |
| ·The Euler equations and the approximations for the minimizers | 第85-92页 |
| Chapter 6 Existence of the solutions for semilinear equations and estimates of the eigenvalues on Heisenberg group | 第92-117页 |
| ·Existence of the solutions for the semilinear subelliptic equations on the Heisenberg group | 第92-106页 |
| ·Estimations of the eigenvalues for the subelliptic operators on the Heisenberg group | 第106-117页 |
| Acknowledgements | 第117-118页 |
| References | 第118-124页 |
