Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities

Bedford, Eric, 1989, Uniqueness for the complex Monge-Ampère equation for functions of logarithmic growth, Indiana Univ. Math. J., 38, 455, 10.1512/iumj.1989.38.38021

Berman, Robert J., 2013, A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics, Adv. Math., 248, 1254, 10.1016/j.aim.2013.08.024

B. Berndtsson, A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem. arXiv:1103.0923.

Błocki, Zbigniew, 2003, Uniqueness and stability for the complex Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J., 52, 1697, 10.1512/iumj.2003.52.2346

Calabi, Eugenio, 1958, Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens, Michigan Math. J., 5, 105

F. Campana, H. Guenancia, and M. Paun, Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields. arXiv:1104.4879.

Cheeger, Jeff, 2000, On the structure of spaces with Ricci curvature bounded below. II, J. Differential Geom., 54, 13

Chen, Xiuxiong, 2000, On the lower bound of the Mabuchi energy and its application, Internat. Math. Res. Notices, 607, 10.1155/S1073792800000337

X-X. Chen, S. Donaldson, and S. Sun, Kähler-Einstein metrics and stability. arXiv:1210.7494. To appear in Int. Math. Res. Not (2013).

Cheng, Shiu Yuen, 1977, On the regularity of the Monge-Ampère equation 𝑑𝑒𝑡(∂²𝑢/∂𝑥ᵢ∂𝑠𝑥ⱼ)=𝐹(𝑥,𝑢), Comm. Pure Appl. Math., 30, 41, 10.1002/cpa.3160300104

Donaldson, S. K., 2012, Kähler metrics with cone singularities along a divisor, 49, 10.1007/978-3-642-28821-0_4

Evans, Lawrence C., 1982, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math., 35, 333, 10.1002/cpa.3160350303

Eyssidieux, Philippe, 2009, Singular Kähler-Einstein metrics, J. Amer. Math. Soc., 22, 607, 10.1090/S0894-0347-09-00629-8

D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order. Springer, 1998.

T. D. Jeffres, R. Mazzeo, and Y. Rubinstein, Kähler-Einstein metrics with edge singularities. arXiv:1105.5216.

Kołodziej, Sławomir, 1998, The complex Monge-Ampère equation, Acta Math., 180, 69, 10.1007/BF02392879

Kołodziej, Sławomir, 2003, The Monge-Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J., 52, 667, 10.1512/iumj.2003.52.2220

Krylov, N. V., 1982, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat., 46, 487

C. Li and S. Sun, Conical Kähler-Einstein metric revisited. arXiv:1207.5011.

Li, Haozhao, 2008, On the lower bound of the 𝐾-energy and 𝐹-functional, Osaka J. Math., 45, 253

Lu, Yung-chen, 1968, Holomorphic mappings of complex manifolds, J. Differential Geometry, 2, 299

J. Song and X-W. Wang, The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality. arXiv:1207.4839.

Székelyhidi, Gábor, 2011, Greatest lower bounds on the Ricci curvature of Fano manifolds, Compos. Math., 147, 319, 10.1112/S0010437X10004938

Tian, G., 1990, Complete Kähler manifolds with zero Ricci curvature. I, J. Amer. Math. Soc., 3, 579, 10.2307/1990928

Yau, Shing Tung, 1978, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math., 31, 339, 10.1002/cpa.3160310304