Yau's solution of the Calabi conjecture gave an essentially complete answer to the question of how Kähler metrics on complex manifolds of nonpositive first Chern class can be deformed into Kähler-Einstein metrics. Akito Futaki showed that the existence of holomorphic vector fields can act as an obstruction to the extension of these results to the case when the complex manifold has positive first Chern class. A proposal of Calabi's, appearing in Yau's "Problem section", was that Kähler-Einstein metrics exist on any compact Kähler manifolds with positive first Chern class which admit no holomorphic vector fields. During the 1980s, Yau came to believe that this criterion would not be sufficient, and that the existence of Kähler-Einstein metrics in this setting must be linked to stability of the complex manifold in the sense of geometric invariant theory. Yau's understanding of this question was updated in the 1990s publication "Open problems in geometry". Subsequent research of Gang Tian and Simon Donaldson refined this conjecture, which became known as the "Yau-Tian-Donaldson conjecture." The problem was resolved in 2015 due to Xiuxiong Chen, Donaldson, and Song Sun, who were awarded the Oswald Veblen prize for their work.