Kähler-Einstein metrics with edge singularities

DOI10.4007/annals.2016.183.1.3zbMath1337.32037arXiv1105.5216OpenAlexW3104436991MaRDI QIDQ5962626

Thalia D. Jeffres, Yanir A. Rubinstein, Rafe R. Mazzeo

Publication date: 15 February 2016

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5216

zbMATH Keywords

edge singularitiesKähler-Einstein metricsdegenerate Monge-Ampère equationRicci continuity method

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler-Einstein manifolds (32Q20)

Related Items

Kähler-Einstein metrics and Archimedean zeta functions ⋮ On large deviation principles and the Monge-Ampère equation (following Berman, Hultgren) ⋮ Calabi-Yau metrics with conical singularities along line arrangements ⋮ Bounded Ricci curvature and positive scalar curvature under Ricci flow ⋮ Families of singular Kähler-Einstein metrics ⋮ On the Cheltsov-Rubinstein conjecture ⋮ A third derivative estimate for Monge-Ampere equations with conic singularities ⋮ On the existence of constant scalar curvature Kähler metric: a new perspective ⋮ Spectral geometry on manifolds with fibred boundary metrics. II: Heat kernel asymptotics ⋮ The continuity method to deform cone angle ⋮ Convergence of the Kähler-Ricci iteration ⋮ On the stability of extensions of tangent sheaves on Kähler-Einstein Fano/Calabi-Yau pairs ⋮ Smooth approximations of the conical Kähler-Ricci flows ⋮ Kähler-Einstein metrics and volume minimization ⋮ On uniform K-stability for some asymptotically log del Pezzo surfaces ⋮ Kiselman's principle, the Dirichlet problem for the Monge-Ampère equation, and rooftop obstacle problems ⋮ Non-existence of Yamabe minimizers on singular spheres ⋮ The twisted Kähler-Ricci flow ⋮ From Monge-Ampère equations to envelopes and geodesic rays in the zero temperature limit ⋮ Classification of strongly asymptotically log del Pezzo flags and surfaces ⋮ On convergence to a football ⋮ On the boundary behavior of Kähler-Einstein metrics on log canonical pairs ⋮ Bounding diameter of conical Kähler metric ⋮ Asymptotic expansions of complete Kähler-Einstein metrics with finite volume on quasi-projective manifolds ⋮ Analysis aspects of Ricci flow on conical surfaces ⋮ Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces ⋮ Connecting toric manifolds by conical Kähler-Einstein metrics ⋮ Asymptotically log Fano varieties ⋮ Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds ⋮ The complex Hessian equations with gradient terms on Hermitian manifolds ⋮ Second-order estimates for collapsed limits of Ricci-flat Kähler metrics ⋮ On the regularity problem of complex Monge-Ampere equations with conical singularities ⋮ Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds ⋮ Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties ⋮ \(K\)-stability of Fano threefolds of rank 2 and degree 14 as double covers ⋮ Kähler metrics with cone singularities along a divisor of bounded Ricci curvature ⋮ Conical Kähler-Einstein metrics revisited ⋮ Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor ⋮ Positive scalar curvature with skeleton singularities ⋮ Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics ⋮ \(\sigma_2\) Yamabe problem on conic 4-spheres ⋮ Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors ⋮ Small angle limits of Hamilton's footballs ⋮ Modified Futaki invariant and equivariant Riemann-Roch formula ⋮ High-Dimensional Convex Sets Arising in Algebraic Geometry ⋮ On the body of ample angles of asymptotically log Fano varieties ⋮ A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics ⋮ K-stability and birational models of moduli of quartic \(K3\) surfaces ⋮ The Ricci continuity method for the complex Monge-Ampère equation, with applications to Kähler-Einstein edge metrics ⋮ Geometry of twisted Kähler-Einstein metrics and collapsing ⋮ Kähler-Einstein metrics ⋮ Expansion formula for complex Monge-Ampère equation along cone singularities ⋮ On a twisted conical Kähler-Ricci flow ⋮ On Kähler-Einstein surfaces with edge singularities ⋮ Dahlberg's theorem in higher co-dimension ⋮ Kähler-Einstein metrics on stable varieties and log canonical pairs ⋮ Tian’s Properness Conjectures:An Introduction to Kähler Geometry ⋮ Kähler-Einstein metrics emerging from free fermions and statistical mechanics ⋮ Cusp Kähler-Ricci flow on compact Kähler manifolds ⋮ Stability of Ricci de Turck flow on singular spaces ⋮ The modified cusp Kähler-Ricci flow and soliton ⋮ Edges, orbifolds, and Seiberg-Witten theory ⋮ Variation of singular Kähler-Einstein metrics: positive Kodaira dimension ⋮ A scalar curvature bound along the conical Kähler-Ricci flow ⋮ On the curvature of conic Kähler-Einstein metrics ⋮ Conical Kähler-Ricci flows on Fano manifolds ⋮ The Green's function for equations with conic metrics ⋮ Local models for conical Kähler-Einstein metrics ⋮ On expansions of Ricci flat ALE metrics in harmonic coordinates about the infinity ⋮ Kähler-Einstein metrics: old and new ⋮ The partial \(C^0\)-estimate along a general continuity path and applications ⋮ On the long time behaviour of the conical Kähler-Ricci flows ⋮ The \(C^{2,\alpha }\)-estimate for conical Kähler-Ricci flow ⋮ Sphere theorems for RCD and stratified spaces ⋮ Conic Kähler-Einstein metrics along simple normal crossing divisors on Fano manifolds ⋮ Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent cones ⋮ Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations ⋮ Ricci de Turck flow on singular manifolds ⋮ Stratified spaces and synthetic Ricci curvature bounds ⋮ Kähler-Einstein metrics with edge singularities ⋮ Pseudodifferential operators on manifolds with fibred corners ⋮ Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry ⋮ Families of conic Kähler-Einstein metrics ⋮ Existence of weak conical Kähler-Einstein metrics along smooth hypersurfaces ⋮ Kähler-Einstein metrics: from cones to cusps ⋮ Maximal time existence of unnormalized conical Kähler-Ricci flow ⋮ Metric contraction of the cone divisor by the conical Kähler-Ricci flow ⋮ Long-time existence of the edge Yamabe flow ⋮ 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 ⋮ The Schwarz lemma: an odyssey ⋮ Geodesics in the space of singular Kähler potentials ⋮ The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties ⋮ Stability of the conical Kähler-Ricci flows on Fano manifolds ⋮ Perelman’s entropies for manifolds with conical singularities ⋮ Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric ⋮ Kähler-Einstein metrics on Fano manifolds ⋮ Kähler-Einstein metrics with prescribed singularities on Fano manifolds ⋮ Schauder estimates for equations with cone metrics, I ⋮ Orbifold stability and Miyaoka-Yau inequality for minimal pairs ⋮ On Kähler conformal compactifications of \(U(n)\)-invariant ALE spaces ⋮ The moduli space of asymptotically cylindrical Calabi-Yau manifolds ⋮ \(C^{2,\alpha}\)-estimate for Monge-Ampère equations with Hölder-continuous right hand side ⋮ K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics

Cites Work

• A variational approach to complex Monge-Ampère equations
• Analytic torsion on manifolds with edges
• The Yamabe problem on stratified spaces
• Monge-Ampère equations in big cohomology classes
• Asymptotics of complete Kähler metrics of finite volume on quasiprojective manifolds
• Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité
• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics
• Kähler-Einstein metrics of negative Ricci curvature on general quasi-projective manifolds
• On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
• K-energy maps integrating Futaki invariants
• Heat kernel estimates and lower bound of eigenvalues
• Boundary behaviour of the complex Monge-Ampère equation
• The Dirichlet problem for a complex Monge-Ampère equation
• Kähler-Einstein metrics with positive scalar curvature
• Uniqueness of Kähler-Einstein cone metrics
• Heat kernel asymptotics on manifolds with conic singularities
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• The K-energy on hypersurfaces and stability
• A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
• The moduli space of asymptotically cylindrical Calabi-Yau manifolds
• A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
• Generalized doubling meets Poincaré
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• Smooth and Singular Kähler–Einstein Metrics
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS
• Point Singularities and Conformal Metrics on Riemann Surfaces
• On the existence of solutions of a class of Monge-Ampére equations
• A General Schwarz Lemma for Kahler Manifolds
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• Elliptic theory of differential edge operators I
• ON STABILITY OF THE TANGENT BUNDLES OF FANO VARIETIES
• Liouville Equation and Spherical Convex Polytopes
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Uniqueness and stability for the complex Monge-Ampere equation on compact Kahler manifolds
• Sobolev met Poincaré
• Elliptic theory of differential edge operators II: boundary value problems
• Remarks on logarithmic K-stability
• K‐Stability and Kähler‐Einstein Metrics
• Kähler Metrics with Cone Singularities Along a Divisor
• Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
• Ricci Flat Kähler Metrics with Edge Singularities
• 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
• The complex Monge-Ampère equation and pluripotential theory
• Harmonic Mappings of Riemannian Manifolds
• Complete Kahler Manifolds with Zero Ricci Curvature. I
• Holomorphic mappings of complex manifolds
• Kähler-Einstein metrics with edge singularities
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item