The case of Kähler surfaces was revisited by Tian in 1990, giving a complete resolution of the Kähler-Einstein problem in that context. The main technique was to study the possible geometric degenerations of a sequence of Kähler-Einstein metrics, as detectable by the Gromov–Hausdorff convergence. Tian adapted many of the technical innovations of Karen Uhlenbeck, as developed for Yang-Mills connections, to the setting of Kähler metrics.
The case of Kähler surfaces was revisited by Tian in 1990, providing a complete resolution to the Kähler-Einstein problem within that context. The primary technique involved analyzing potential geometric degenerations of a sequence of Kähler-Einstein metrics, as identified through Gromov–Hausdorff convergence. Tian adapted many of the technical advancements of Karen Uhlenbeck, as developed for Yang-Mills connections, to the setting of Kähler metrics.