| 1 Preface: Background | 第8-14页 |
| 2 Basic Material on Sub-Riemannian Manifolds | 第14-22页 |
| 2.1 Sub-Riemannian Manifolds | 第14-17页 |
| 2.2 Examples | 第17-22页 |
| 2.2.1 Contact Manifolds | 第17页 |
| 2.2.2 Carnot Groups | 第17-22页 |
| 3 Geometry of Generalized Heisenberg Groups | 第22-37页 |
| 3.1 Properties of Sub-Riemannian Geodesics | 第23-30页 |
| 3.2 The Sub-Riemannian Isometry Groups | 第30-35页 |
| 3.3 The Jacobian of Changing Variables Along Geodesics | 第35-37页 |
| 4 Horizontal Connection and Mean Curvatures | 第37-58页 |
| 4.1 Introduction | 第37-41页 |
| 4.2 Horizontal Tangent Bundle and Connectivity | 第41-48页 |
| 4.3 Horizontal Connection and the Horizontal Mean Curvature | 第48-58页 |
| 5 Sobolev Classes between CC Spaces | 第58-76页 |
| 5.1 Sobolev Functions Defined on CC Spaces | 第59-61页 |
| 5.2 Sobolev Classes from CC Spaces to Separable Metric Spaces | 第61-76页 |
| 5.2.1 Equivalence of Sobolev Classes | 第61-66页 |
| 5.2.2 Basic Properties of Sobolev Mappings between CC Spaces | 第66-76页 |
| 6 Energy Minimizers from CC Spaces | 第76-114页 |
| 6.1 Introduction | 第76-81页 |
| 6.2 The Choice of Energy Functionals | 第81-87页 |
| 6.2.1 The Energy Functional of Korevaar-Schoen | 第81-84页 |
| 6.2.2 Our Energy Functional | 第84-87页 |
| 6.3 Precompactness and Trace Theorems for Sobolev Mappings | 第87-92页 |
| 6.4 Existence of Energy Minimizers in the General Case | 第92-94页 |
| 6.5 Regularity of Energy Minimizers into NPC Spaces | 第94-103页 |
| 6.5.1 Generalized Dirichlet Forms | 第94-98页 |
| 6.5.2 Spaces of Nonpositive Curvature in the Sense of Alexandrov | 第98-99页 |
| 6.5.3 Removing the Noncharacteristic Condition and Uniqueness of Minimizer | 第99-101页 |
| 6.5.4 Holder Continuity of Energy Minimizer | 第101-103页 |
| 6.6 Regularity of Minimizers: the Heisenberg Group Target | 第103-114页 |
