Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof

Abstract

This is the third and final paper in a series which establish results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2π. We also put all our technical results together to complete the proof of the main theorem that if a K-stable Fano manifold admits a Kahler-Einstein metric.

References in corpus (7)

• The Space of Kähler metrics (II)
• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Conical Kahler-Einstein metric revisited
• Singular Kahler-Einstein metrics
• Ricci flow on Orbifold

Cited by in corpus (35)

• Space of Ricci flows (II)
• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
• On the moduli of Kahler-Einstein Fano manifolds
• Kähler-Einstein metrics on group compactifications
• Asymptotically log Fano varieties
• Riemannian geometry of Kahler-Einstein currents
• Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors
• Smooth approximations of the Conical Kahler-Ricci flows
• Bessel Functions, Heat Kernel and the Conical Kähler-Ricci Flow
• The conical Kähler-Ricci flow on Fano manifolds
• Geodesics in the space of Kähler cone metrics
• On the long time behaviour of the Conical Kähler- Ricci flows
• Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
• Extremal Kähler metrics
• Connecting toric manifolds by conical Kahler-Einstein metrics
• Regularity of Kähler-Ricci flows on Fano manifolds
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Unnormalize conical Kähler-Ricci flow
• Existence of Weak Conical Kähler-Einstein Metrics Along Smooth Hypersurfaces
• Alpha-invariant of Toric Line Bundles
• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow
• Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• Regularity of Kähler-Ricci flow
• Alpha invariants and K-stability for general polarisations of Fano varieties
• Note on Poincaré type Kähler metrics and Futaki characters
• On the Spectrum of weighted Laplacian operator and its application to uniqueness of Kähler Einstein metrics
• Edges, Orbifolds, and Seiberg-Witten Theory
• Interior Estimates for the $n$-dimensional Abreu's Equation
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side
• Fano manifolds with weak almost Kähler-Ricci solitons
• Removable singularities of the CscK metric
• On the modified Futaki invariant of complete intersections in projective spaces
• Hyperkahler metric and GMN ansatz on focus-focus fibrations