| Popis: |
In this chapter, we discuss the Yau–Tian–Donaldson conjecture from a historical point of view. In Sect. 6.1, we briefly discuss the Calabi conjecture. The unsolved case of the Calabi conjecture motivates the Yau–Tian–Donaldson conjecture in Kahler–Einstein cases. As mentioned in Sect. 6.2, the Yau–Tian–Donaldson conjecture in Kahler–Einstein cases was solved affirmatively by Chen, Donaldson and Sun and by Tian. In Sect. 6.3, we define K-energy and modified K-energy for compact Kahler manifolds. This concept allows us to state the recent results of Chen and Cheng and of He on the existence of CSC Kahler metrics and extremal Kahler metrics. Finally, in Sect. 6.4, various versions of the Yau–Tian–Donaldson conjecture will be considered in extremal Kahler cases. |
