Kähler-Einstein metrics

DOI10.1090/pspum/099/01745zbMath1448.53074arXiv1710.06042OpenAlexW2594571379MaRDI QIDQ5136626

Publication date: 27 November 2020

Published in: Proceedings of Symposia in Pure Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.06042

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Kähler-Einstein manifolds (32Q20) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

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RC-positivity and scalar-flat metrics on ruled surfaces ⋮ K-stability of Fano varieties: an algebro-geometric approach

Cites Work

K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
Bergman kernel along the Kähler-Ricci flow and Tian's conjecture
Completion of the moduli space for polarized Calabi-Yau manifolds
Kähler-Einstein metrics along the smooth continuity method
Alpha invariant and K-stability of \(\mathbb Q\)-Fano varieties
Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry
Kähler-Einstein metrics on stable varieties and log canonical pairs
Compact moduli spaces of Kähler-Einstein Fano varieties
K-stability for Fano manifolds with torus action of complexity 1
Kähler-Einstein metrics on group compactifications
Regularity of Kähler-Ricci flows on Fano manifolds
Relative K-stability of extremal metrics
Homogeneous spaces and equivariant embeddings
Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
Stability of valuations: higher rational rank
Calabi-Yau manifolds with isolated conical singularities
Quantization and the Hessian of Mabuchi energy
Bergman approximations of harmonic maps into the space of Kähler metrics on toric varieties
Existence and deformations of Kähler-Einstein metrics on smoothable \(\mathbb{Q}\)-Fano varieties
Extremal metrics and lower bound of the modified K-energy
On Calabi's conjecture for complex surfaces with positive first Chern class
Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics
Stability of valuations and Kollár components
Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité
Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature
Polyhedral divisors and algebraic torus actions
Blowing up and desingularizing constant scalar curvature Kähler manifolds
The Mabuchi geometry of finite energy classes
Regularity of Einstein manifolds and the codimension 4 conjecture
Harmonic discs of solutions to the complex homogeneous Monge-Ampère equation
On a set of polarized Kähler metrics on algebraic manifolds
Convergence and rigidity of manifolds under Ricci curvature bounds
Valuations and plurisubharmonic singularities
Hamiltonian 2-forms in Kähler geometry. III: Extremal metrics and stability
Obstructions to the existence of Sasaki-Einstein metrics
Calabi flow and projective embeddings
K-stability of constant scalar curvature Kähler manifolds
Some numerical results in complex differential geometry
Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds
On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
K-energy maps integrating Futaki invariants
Infinite determinants, stable bundles and curvature
Threefolds and deformations of surface singularities
Some symplectic geometry on compact Kähler manifolds. I
Remarks on the existence problem of positive Kähler-Einstein metrics
Connections with \(L^ p \)bounds on curvature
Kähler-Einstein metrics and the generalized Futaki invariant
The Dirichlet problem for a complex Monge-Ampère equation
Distribution of zeros of random and quantum chaotic sections of positive line bundles
Über eine bemerkenswerte Hermitesche Metrik
Ricci curvature and volume convergence
Kähler-Einstein metrics with positive scalar curvature
On the structure of spaces with Ricci curvature bounded below. I
The complex Monge-Ampère equation
Scalar curvature and projective embeddings. I
On the structure of spaces with Ricci curvature bounded below. II
On the structure of spaces with Ricci curvature bounded below. III
The space of Kähler metrics.
Convergence of Ricci flows with bounded scalar curvature
Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
Relative K-stability for Kähler manifolds
Kähler-Einstein metrics and volume minimization
On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics
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
K-semistability of cscK manifolds with transcendental cohomology class
An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds. I.
Scalar curvature and stability of toric varieties.
Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth
A new proof of a theorem of Narasimhan and Seshadri
Three-manifolds with positive Ricci curvature
An obstruction to the existence of Einstein Kaehler metrics
Holomorphic discs and the complex Monge-Ampère equation.
Kähler--Ricci solitons on toric manifolds with positive first Chern class
Lower bounds on Ricci curvature and quantitative behavior of singular sets
The GIT stability of polarized varieties via discrepancy
A generalization of the Ross-Thomas slope theory
Height and GIT weight
On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties
Relative Chow stability and extremal metrics
Special test configuration and \(K\)-stability of Fano varieties
Curvature functions for compact 2-manifolds
\(K\)-stability of cubic threefolds
Degenerations of \(\mathbf{C}^n\) and Calabi-Yau metrics
A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
Filtrations and test-configurations
Geodesics in the space of Kähler metrics
Curvature of vector bundles associated to holomorphic fibrations
Test configurations for \(k\)-stability and geodesic rays
Lower bounds on the Calabi functional
An obstruction to the existence of constant scalar curvature Kähler metrics
Stable and unitary vector bundles on a compact Riemann surface
Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
The partial 𝐶⁰-estimate along the continuity method
Space of Kähler Metrics (V) – Kähler Quantization
Space of Ricci Flows I
Alpha Invariants and K-Stability for General Polarizations of Fano Varieties
Moduli of varieties of general type
Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics
Constant Scalar Curvature Kahler Metric Obtains the Minimum of K-energy
Regularity of geodesic rays and Monge-Ampère equations
Singular Kähler-Einstein metrics
Morse theory and geodesics in the space of Kähler metrics
Degeneration of Kähler–Ricci Solitons
Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
K-stability of Fano spherical varieties
Anti Self-Dual Yang-Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
Extremal metrics and K-stability
A study of the Hilbert-Mumford criterion for the stability of projective varieties
Kähler–Einstein Metrics and Stability
Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds
The Kähler-Ricci flow and K-polystability
Scalar curvature and projective embeddings, II
Complex Monge-Ampere and Symplectic Manifolds
On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
Geometric Invariant Theory
Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold
Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS
Total log canonical thresholds and generalized Eckardt points
On the existence of hermitian-yang-mills connections in stable vector bundles
The Yang-Mills equations over Riemann surfaces
Test configurations and Okounkov bodies
On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch
Regularity of weak minimizers of the K-energy and applications to properness and K-stability
A variational approach to the Yau–Tian–Donaldson conjecture
Kähler Metrics with Cone Singularities Along a Divisor
The Ding Functional, Berndtsson Convexity and Moment Maps
Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
Test configurations and Geodesic rays
b-Stability and Blow-Ups
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
Stability, birational transformations and the Kahler-Einstein problem
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
Degeneration of Kahler-Ricci solitons on Fano manifolds
Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
Removable singularities in Yang-Mills fields
Geometric criterion for Gieseker-Mumford stability of polarized manifolds
Kähler-Einstein metrics with edge singularities
Compact moduli spaces of del Pezzo surfaces and Kähler-Einstein metrics
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