| §1 Preparations and basic material. | 第7-22页 |
| §1.1 Hermitian geometry | 第7-14页 |
| §1.2 Theory of elliptic operators and Sobolev spaces | 第14-19页 |
| §1.3 Hermitian-Einstein metrics and Stability | 第19-22页 |
| §2 Existence of Hermitian-Einstein metric in stable Higgs bundle | 第22-43页 |
| §2.1 The way of the continuity method | 第22-27页 |
| §2.2 The continuity method: continued | 第27-35页 |
| §2.3 The construction of a destablising sub-Higgs-sheaf | 第35-41页 |
| §2.4 Related to Kobayashi-Hitchin correspondence | 第41-43页 |
| §3 A Kazdan-Warner type equation on compact complex manifold | 第43-48页 |
| §3.1 Lemmas and Proof of Theorems | 第44-48页 |
| References | 第48-50页 |
| 后记 | 第50页 |
