Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
From MaRDI portal
Publication:2420201
DOI10.1515/crelle-2016-0033zbMath1430.14083arXiv1111.7158OpenAlexW2963754085WikidataQ103487178 ScholiaQ103487178MaRDI QIDQ2420201
Robert J. Berman, Sébastien Boucksom, Ahmed Zeriahi, Vincent Guedj, Philippe Eyssidieux
Publication date: 5 June 2019
Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1111.7158
Global differential geometry of Hermitian and Kählerian manifolds (53C55) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Fano varieties (14J45) Kähler-Einstein manifolds (32Q20) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)
Related Items
Mabuchi's soliton metric and relative D-stability ⋮ The strong topology of \(\omega \)-plurisubharmonic functions ⋮ Continuity of Monge-Ampère potentials with prescribed singularities ⋮ Families of singular Kähler-Einstein metrics ⋮ Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's ``hypothèse fondamentale ⋮ Global pluripotential theory over a trivially valued field ⋮ Singular Kähler-Einstein metrics on \(\mathbb{Q}\)-Fano compactifications of Lie groups ⋮ The continuity method to deform cone angle ⋮ On cscK resolutions of conically singular cscK varieties ⋮ Convergence of the Kähler-Ricci iteration ⋮ Extremal potentials and equilibrium measures for collections of Kähler classes ⋮ Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties ⋮ From Monge-Ampère equations to envelopes and geodesic rays in the zero temperature limit ⋮ Geodesic rays and stability in the lowercase cscK problem ⋮ K-stability of Gorenstein Fano group compactifications with rank two ⋮ Measure preserving holomorphic vector fields, invariant anti-canonical divisors and Gibbs stability ⋮ Geodesic distance and Monge-Ampére measures on contact sets ⋮ Kähler-Einstein metrics along the smooth continuity method ⋮ Complex Monge-Ampère equations on quasi-projective varieties ⋮ Regularizing properties of the twisted Kähler-Ricci flow ⋮ Tian's partial \(C^0\)-estimate implies Hamilton-Tian's conjecture ⋮ Generalized Kähler-Ricci flow on toric Fano varieties ⋮ Geometric pluripotential theory on Sasaki manifolds ⋮ On the Briançon-Skoda theorem for analytic local rings with singularities ⋮ The Mabuchi geometry of finite energy classes ⋮ Comparison of the Calabi and Mabuchi geometries and applications to geometric flows ⋮ \(L^1\) metric geometry of big cohomology classes ⋮ Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds ⋮ The Kähler-Ricci flow on log canonical pairs of general type ⋮ Kähler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional ⋮ On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations ⋮ Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs ⋮ Bergman kernels for a sequence of almost Kähler-Ricci solitons ⋮ Kähler-Einstein metrics and Archimedean zeta functions ⋮ Weighted K-stability and coercivity with applications to extremal Kähler and Sasaki metrics ⋮ Quasi-monotone convergence of plurisubharmonic functions ⋮ Continuity method with movable singularities for classical complex Monge-Ampere equations ⋮ Conical Kähler-Einstein metrics revisited ⋮ On the regularity of conical Calabi–Yau potentials ⋮ Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics ⋮ Quasi-plurisubharmonic envelopes 3: solving Monge-Ampère equations on Hermitian manifolds ⋮ ACC for local volumes and boundedness of singularities ⋮ Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties ⋮ Kähler-Ricci flow on Fano manifolds ⋮ Canonical Kähler metrics and stability of algebraic varieties ⋮ The probabilistic vs the quantization approach to Kähler-Einstein geometry ⋮ Geometric flow, multiplier ideal sheaves and optimal destabilizer for a Fano manifold ⋮ \(L^2\) extension of holomorphic functions for log canonical pairs ⋮ Smooth approximation of twisted Kähler-Einstein metrics ⋮ On the singularity type of full mass currents in big cohomology classes ⋮ Geometric methods of complex analysis. Abstracts from the workshop held May 16--22, 2021 (hybrid meeting) ⋮ Ricci curvature in Kähler geometry ⋮ On \(L^2\) extension from singular hypersurfaces ⋮ Reductivity of the automorphism group of K-polystable Fano varieties ⋮ Geodesic rays and Kähler–Ricci trajectories on Fano manifolds ⋮ Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry ⋮ On the existence of conic Kähler-Einstein metrics ⋮ Delta-invariants for Fano varieties with large automorphism groups ⋮ The long-time behavior of modified Calabi flow ⋮ Ricci flat Kähler metrics on rank two complex symmetric spaces ⋮ Kähler-Einstein metrics on stable varieties and log canonical pairs ⋮ Ricci iteration on homogeneous spaces ⋮ Tian’s Properness Conjectures:An Introduction to Kähler Geometry ⋮ Kähler–Einstein Metrics on Toric Manifolds and G-manifolds ⋮ Existence of Kähler-Ricci solitons on smoothable \(\mathbb{Q}\)-Fano varieties ⋮ Stability of valuations: higher rational rank ⋮ On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows ⋮ Basis divisors and balanced metrics ⋮ On the constant scalar curvature Kähler metrics (II)—Existence results ⋮ Algebraicity of the metric tangent cones and equivariant K-stability ⋮ Uniqueness of constant scalar curvature Kähler metrics with cone singularities. I: Reductivity ⋮ Convergence of weak Kähler-Ricci flows on minimal models of positive Kodaira dimension ⋮ Variation of singular Kähler-Einstein metrics: positive Kodaira dimension ⋮ K-stability of Fano varieties: an algebro-geometric approach ⋮ Conical Kähler-Ricci flows on Fano manifolds ⋮ The volume of singular Kähler–Einstein Fano varieties ⋮ The volume of Kähler-Einstein Fano varieties and convex bodies ⋮ Generalized Matsushima's theorem and Kähler-Einstein cone metrics ⋮ A variational approach to the Yau–Tian–Donaldson conjecture ⋮ Regularity of Kähler-Ricci flows on Fano manifolds ⋮ On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties ⋮ Pluripotential Kähler-Ricci flows ⋮ Monge-Ampère iteration ⋮ Geometry and topology of the space of Kähler metrics on singular varieties ⋮ Finite pluricomplex energy measures ⋮ Finite entropy vs finite energy ⋮ On the spectrum of weighted Laplacian operator and its application to uniqueness of Kähler Einstein metrics ⋮ Continuity of delta invariants and twisted Kähler-Einstein metrics ⋮ Geometric pluripotential theory on Kähler manifolds ⋮ Orbifold regularity of weak Kähler-Einstein metrics ⋮ Kähler-Einstein metrics: from cones to cusps ⋮ Compactness of Kähler metrics with bounds on Ricci curvature and \({\mathcal{I}}\) functional ⋮ The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics ⋮ \(G\)-uniform stability and Kähler-Einstein metrics on Fano varieties ⋮ \(L^1\) metric geometry of potentials with prescribed singularities on compact Kähler manifolds ⋮ On a family of quasimetric spaces in generalized potential theory ⋮ Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof ⋮ Analytic adjoint ideal sheaves associated to plurisubharmonic functions II ⋮ The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties ⋮ Uniformly strong convergence of Kähler-Ricci flows on a Fano manifold ⋮ Kähler-Einstein metrics on Fano manifolds ⋮ A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry ⋮ Kähler-Einstein metrics with prescribed singularities on Fano manifolds ⋮ Orbifold stability and Miyaoka-Yau inequality for minimal pairs ⋮ Weak solutions to degenerate complex Monge-Ampère flows. II ⋮ K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Kähler-Einstein metrics along the smooth continuity method
- A variational approach to complex Monge-Ampère equations
- Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry
- Monge-Ampère equations in big cohomology classes
- Plurisubharmonische Funktionen in komplexen Räumen
- Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
- Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics
- The Kähler-Ricci flow with positive bisectional curvature
- Growth of balls of holomorphic sections and energy at equilibrium
- Large deviations techniques and applications.
- Regularity properties of the degenerate Monge-Ampère equations on compact Kähler manifolds
- On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
- Existence and degeneration of Kähler-Einstein metrics on minimal algebraic varieties of general ype
- Kähler-Einstein metrics on complex surfaces with \(C_ 1>0\)
- Remarks on the existence problem of positive Kähler-Einstein metrics
- Fine topology, Šilov boundary, and \((dd^ c)^ n\)
- Linear complementary inequalities for orders of germs of analytic functions
- Kähler-Einstein metrics and the generalized Futaki invariant
- The Levi problem on complex spaces with singularities
- Kähler-Einstein metrics with positive scalar curvature
- On the singularities of spaces with bounded Ricci curvature
- Special test configuration and \(K\)-stability of Fano varieties
- A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
- Stability of solutions to complex Monge-Ampère equations in big cohomology classes
- A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
- The weighted Monge-Ampère energy of quasiplurisubharmonic functions
- Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres
- Multiplier ideal sheaves and the Kähler-Ricci flow
- On the lower bound of the \(K\)-energy and \(F\)-functional
- Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions
- Singular semipositive metrics in non-Archimedean geometry
- Regularizing Properties of the Kähler–Ricci Flow
- Canonical measures and Kähler-Ricci flow
- Existence of Einstein Metrics on Fano Manifolds
- Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics
- Viscosity solutions to degenerate complex monge-ampère equations
- Lectures on Stability and Constant Scalar Curvature
- Singular Kähler-Einstein metrics
- The Calabi–Yau Theorem
- Ricci iterations on Kähler classes
- Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
- Symmetries, quotients and Kähler-Einstein metrics
- Elements d'histoire des matehmatique
- Convergence of Kähler-Ricci flow
- On regularization of plurisubharmonic functions on manifolds
- Kähler–Einstein Metrics and Stability
- BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)
- CHOW STABILITY CRITERION IN TERMS OF LOG CANONICAL THRESHOLD
- The Moser-Trudinger inequality on Kähler-Einstein manifolds
- Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines
- On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
- Singularities of Pairs
- ON THE VOLUME OF A LINE BUNDLE
- Extension of plurisubharmonic functions with growth control
- K‐Stability and Kähler‐Einstein Metrics
- K-stability Implies CM-stability
- Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
- Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
- Sous-ensembles analytiques d'ordre fini ou infini dans $C^n$
- Kähler-Einstein metrics with edge singularities