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 (6)

• 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 (7)

• Riemannian geometry of Kahler-Einstein currents
• Extremal Kähler metrics
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Unnormalize conical Kähler-Ricci flow
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• Regularity of Kähler-Ricci flow
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side