The existence problem of Kähler-Einstein metrics: a grocery

Click here for a discussion on the problem itself.

I.Books on the classical theory

Aubin  Some nonlinear problems in Riemannian geometry

Futaki  Kähler-Einstein Metrics and integral invariants

Siu  Lectures on Hermitian-Einstein Metric for Stable Bundles and Kähler-Einstein Metrics

Tian  Canonical metrics in Kähler geometry

II.Papers

Calabi conjectures for $c_1<0$ and $c_1=0$

Yau  On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I

Lie-theoretical obstructions for $c_1>0$

K-energy and Uniqueness for $c_1>0$

Bando, Mabuchi  Uniqueness of Einstein-Kähler metrics modulo connected group actions

Concrete constructions

$c_1>0$ for complex surfaces

Hitchin-Kobayashi correspondence

Uhlenbeck, Yau  On the existence of Hermitian-Yang-Mills connections in stable vector bundles

Donaldson  Infinite determinants, stable bundles and curvature

Differential-geometric K-stability

Cheeger, Coding, Tian  On the singularities of spaces with bounded Ricci curvature

Algebro-geometric K-stability

Announced proofs for the Yau-Tian-Donaldson conjecture