Ricci curvature in Kähler geometry

Singularities in algebraic geometry (14B05) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Local complex singularities (32S05)

Cites Work

K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
Conical Kähler-Einstein metrics revisited
Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry
Compact moduli spaces of Kähler-Einstein Fano varieties
Examples of asymptotically conical Ricci-flat Kähler manifolds
Existence and deformations of Kähler-Einstein metrics on smoothable \(\mathbb{Q}\)-Fano varieties
On Calabi's conjecture for complex surfaces with positive first Chern class
On a set of polarized Kähler metrics on algebraic manifolds
Canonical Sasakian metrics
Sasaki-Einstein manifolds and volume minimisation
Obstructions to the existence of Sasaki-Einstein metrics
K-stability of constant scalar curvature Kähler manifolds
Kähler-Einstein metrics and integral invariants
Rational connectedness and boundedness of Fano manifolds
Kähler-Einstein metrics and the generalized Futaki invariant
Ricci-flat metrics on the complexification of a compact rank one symmetric space
Kähler-Einstein metrics with positive scalar curvature
On the structure of spaces with Ricci curvature bounded below. I
The space of Kähler metrics.
Minimizing normalized volumes of valuations
K-semistability is equivariant volume minimization
Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs
Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry. II
On the K-stability of Fano varieties and anticanonical divisors
K-semistability for irregular Sasakian manifolds
Scalar curvature and stability of toric varieties.
Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
On the singularities of spaces with bounded Ricci curvature
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Height and GIT weight
Sasaki-Einstein metrics and K-stability
Special test configuration and \(K\)-stability of Fano varieties
On deformations of complex analytic structures. II
A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
Geodesics in the space of Kähler metrics
Weak geodesics in the space of Kähler metrics
Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
A valuative criterion for uniform K-stability of \(\mathbb{Q}\)-Fano varieties
Kähler-Ricci soliton and \(H\)-functional
Frankel conjecture and Sasaki geometry
Alpha Invariants and K-Stability for General Polarizations of Fano Varieties
Algebraic families of constant scalar curvature K\"ahler metrics
Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
Kähler–Einstein Metrics and Stability
On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch
A variational approach to the Yau–Tian–Donaldson conjecture
Kähler Metrics with Cone Singularities Along a Divisor
Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
Vector fields and Ricci curvature
Compact moduli spaces of del Pezzo surfaces and Kähler-Einstein metrics
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