| Frontmatterpp. i–iv |
| Contentsp. v |
| Prefacepp. vii–viii |
| 1 | Gaussian curvature equationpp. 1–8 |
| 2 | Moser–Trudinger inequality (on the sphere)pp. 9–16 |
| 3 | Polyakov formula on compact surfacespp. 17–24 |
| 4 | Conformal covariant operators – Paneitz operatorpp. 25–29 |
| 5 | Functional determinant on 4-manifoldspp. 30–37 |
| 6 | Extremal metrics for the log-determinant functionalpp. 38–49 |
| 7 | Elementary symmetric functionspp. 50–55 |
| 8 | A priori estimates for the regularized equation (∗)δpp. 56–73 |
| 9 | Smoothing via the Yamabe flowpp. 74–78 |
| 10 | Deforming σ2 to a constant functionpp. 79–86 |
| Bibliographypp. 87–92 |
