Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities

Abstract

This is the first of a series of three papers which provide proofs of results announced recently in arXiv:1210.7494.

References in corpus (4)

• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• Conical Kahler-Einstein metric revisited
• Singular Kahler-Einstein metrics
• Kahler-Einstein metrics and stability

Cited by in corpus (15)

• Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
• Geodesics in the space of Kähler cone metrics
• On the long time behaviour of the Conical Kähler- Ricci flows
• Extremal Kähler metrics
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• Alpha invariants and K-stability for general polarisations of Fano varieties
• Note on Poincaré type Kähler metrics and Futaki characters
• Orbifold regularity of weak Kahler-Einstein metrics
• Interior Estimates for the $n$-dimensional Abreu's Equation
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side
• Toric partial density functions and stability of toric varieties