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


Calabi conjectures for c_1<0 and c_1=0 

Yau  Calabi’s conjecture and some new results in algebraic geometry

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

Lie-theoretical obstructions for c_1>0

Matsushima  Sur la structure du groupe d’homéomorphismes analytiques d’une certaine variété káhlérienne

Futaki  An obstruction to the existence of Einstein-Kähler metric

K-energy and Uniqueness for c_1>0

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

Concrete constructions

Siu  The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group

Nadel  Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature

c_1>0 for complex surfaces

Tian, Yau  Kähler-Einstein metrics on complex surfaces with c_1>0

Tian  On Calabi’s conjecture for complex surfaces with positive first Chern class

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

Ding, Tian  Kähler-Einstein metrics and the generalized Futaki invariant

Tian  Kähler-Einstein metrics with positive scalar curvature

Tian  Kähler-Einstein metrics on algebraic manifolds

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

Donaldson  Kähler metrics with cone singularities along a divisor

Berman  A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics

Li, Sun  Conical Kähler-Einstein metric revisited

Algebro-geometric K-stability

Donaldson  Scalar curvature and stability of toric varieties

Donaldson  Lower bounds on the Calabi functional

Stoppa  K-stability of constant scalar curvature Kähler manifolds

Donaldson  Stability, birational transformations and the Kähler-Einstein problem

Sun  Note on K-stability of pairs

Li, Xu  Special test configurations and K-stability of Fano varieties

Donaldson, Sun  Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry

Announced proofs for the Yau-Tian-Donaldson conjecture

Tian  K-stability and Kähler-Einstein metrics

Chen, Donaldson, Sun  Kähler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities

Chen, Donaldson, Sun  Kähler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 \pi

Chen, Donaldson, Sun  Kähler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2 \pi and completion of the main proof


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