[1]

P. Ahag, U. Cegrell, S. Kolodziej, H. H. Pham and A. Zeriahi,
Partial pluricomplex energy and integrability exponents of plurisubharmonic functions,
Adv. Math. 222 (2009), 2036–2058.
Web of ScienceGoogle Scholar

[2]

H. Auvray,
The space of Poincaré type Kähler metrics on the complement of a divisor,
preprint (2011), http://arxiv.org/abs/1109.3159.

[3]

E. Bedford and B. A. Taylor,
A new capacity for plurisubharmonic functions,
Acta Math. 149 (1982), no. 1–2, 1–40.
Google Scholar

[4]

S. Benelkourchi, V. Guedj and A. Zeriahi,
A priori estimates for solutions of Monge–Ampère equations,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008), no. 1, 81–96.
Google Scholar

[5]

R. J. Berman, S. Boucksom, P. Eyssidieux, V. Guedj and A. Zeriahi,
Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties,
preprint (2012), http://arxiv.org/abs/1111.7158.

[6]

R. J. Berman, S. Boucksom, V. Guedj and A. Zeriahi,
A variational approach to complex Monge–Ampère equations,
Publ. Math. Inst. Hautes Études Sci. 117 (2013), 179–245.
Google Scholar

[7]

R. J. Berman and H. Guenancia,
Kähler–Einstein metrics on stable varieties and log canonical pairs,
preprint (2013), http://arxiv.org/abs/1304.2087.

[8]

S. Boucksom, P. Eyssidieux, V. Guedj and A. Zeriahi,
Monge–Ampère equations in big cohomology classes,
Acta Math. 205 (2010), no. 2, 199–262.
Google Scholar

[9]

F. Campana, H. Guenancia and M. Păun,
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields,
Ann. Sci. Éc. Norm. Supér. (4) 46 (2013), no. 6, 879–916.
CrossrefGoogle Scholar

[10]

U. Cegrell,
Pluricomplex energy,
Acta Math. 180 (1998), no. 2, 187–217.
Google Scholar

[11]

U. Cegrell,
The general definition of the complex Monge–Ampère operator,
Ann. Inst. Fourier (Grenoble) 54 (2004), no. 1, 159–179.
Google Scholar

[12]

U. Cegrell, S. Kołodziej and A. Zeriahi,
Subextension of plurisubharmonic functions with weak singularities,
Math. Z. 250 (2005), no. 1, 7–22.
Google Scholar

[13]

X. X. Chen, S. K. Donaldson and S. Sun,
Kähler–Einstein metrics on Fano manifolds, I: Approximation of metrics with cone singularities,
J. Amer. Math. Soc. (2014), 10.1090/S0894-0347-2014-00799-2.
Google Scholar

[14]

X. X. Chen, S. K. Donaldson and S. Sun,
Kähler–Einstein metrics on Fano manifolds, II: Limits with cone angle less than $2\pi $,
J. Amer. Math. Soc. (2014), 10.1090/S0894-0347-2014-00800-6.
Google Scholar

[15]

X. X. Chen, S. K. Donaldson and S. Sun,
Kähler–Einstein metrics on Fano manifolds, III: Limits as cone angle approaches $2\pi $ and completion of the main proof,
preprint (2013), http://arxiv.org/abs/1302.0282.

[16]

J. P. Demailly,
Regularization of closed positive currents of type $(1,1)$ by the flow of a Chern connection,
Contributions to complex analysis and analytic geometry,
Aspects Math. E26,
Vieweg-Verlag, Braunschweig (1994), 105–126.
Google Scholar

[17]

E. Di Nezza and H. C. Lu,
Generalized Monge–Ampère capacities,
preprint (2014), http://arxiv.org/abs/1402.2497;
to appear in Int. Math. Res. Not. IMRN.

[18]

S. Dinew,
Uniqueness in $\mathcal{\mathcal{E}}(X,\omega )$,
J. Funct. Anal. 256 (2009), no. 7, 2113–2122.
Google Scholar

[19]

S. K. Donaldson,
Kähler metrics with cone singularities along a divisor,
Essays in mathematics and its applications,
Springer-Verlag, Heidelberg (2012), 49–79.
Google Scholar

[20]

S. K. Donaldson and S. Sun,
Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry,
preprint (2012), http://arxiv.org/abs/1206.2609.

[21]

P. Eyssidieux, V. Guedj and A. Zeriahi,
Singular Kähler Einstein metrics,
J. Amer. Math. Soc. 22 (2009), no. 3, 607–639.
Google Scholar

[22]

V. Guedj and A. Zeriahi,
Intrinsic capacities on compact Kähler manifolds,
J. Geom. Anal. 15 (2005), no. 4, 607–639.
Google Scholar

[23]

V. Guedj and A. Zeriahi,
The weighted Monge–Ampère energy of quasiplurisubharmonic functions,
J. Funct. Anal. 250 (2007), no. 2, 442–482.
Google Scholar

[24]

V. Guedj and A. Zeriahi,
Stability of solutions to complex Monge–Ampère equations in big cohomology classes,
Math. Res. Lett. 19 (2012), no. 5, 1025–1042.
Google Scholar

[25]

H. J. Hein,
Gravitational instantons from rational elliptic surfaces,
J. Amer. Math. Soc. 25 (2012), no. 2, 355–393.
Google Scholar

[26]

R. Kobayashi,
Kähler–Einstein metric on an open algebraic manifold,
Osaka J. Math. 21 (1984), no. 2, 399–418.
Google Scholar

[27]

S. Kołodziej,
The range of the complex Monge–Ampère operator,
Indiana Univ. Math. J. 43 (1994), no. 4, 1321–1338.
Google Scholar

[28]

S. Kołodziej,
The complex Monge–Ampère equation,
Acta Math. 180 (1998), 69–117.
Google Scholar

[29]

S. Kołodziej,
The complex Monge–Ampère equation on compact Kähler manifolds,
Indiana Univ. Math. J. 52 (2003), no. 3, 667–686.
Google Scholar

[30]

M. Păun,
Regularity properties of the degenerate Monge–Ampère equations on compact Kähler manifolds,
Chin. Ann. Math. Ser. B 29 (2008), no. 6, 623–630.
Google Scholar

[31]

Y. T. Siu,
Lectures on Hermitian–Einstein metrics for stable bundles and Kähler–Einstein metrics,
Birkhäuser-Verlag, Basel 1987.
Google Scholar

[32]

H. Skoda,
Sous-ensembles analytiques d’ordre fini ou infini dans ${\u2102}^{n}$,
Bull. Soc. Math. France 100 (1972), 353–408.
Google Scholar

[33]

G. Tian,
K-stability and Kähler–Einstein metrics,
preprint (2013), http://arxiv.org/abs/1211.4669.

[34]

G. Tian and S. T. Yau,
Existence of Kähler–Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry,
Mathematical aspects of string theory (San Diego 1986),
Adv. Ser. Math. Phys. 1,
World Scientific, Singapore (1987), 574–628.
Google Scholar

[35]

G. Tian and S. T. Yau,
Complete Kähler manifolds with zero Ricci curvature. I,
J. Amer. Math. Soc. 3 (1990), no. 3, 579–609.
Google Scholar

[36]

G. Tian and S. T. Yau,
Complete Kähler manifolds with zero Ricci curvature. II,
Invent. Math. 106 (1991), no. 1, 27–60.
Google Scholar

[37]

H. Tsuji,
Existence and degeneration of Kähler–Einstein metrics on minimal algebraic varieties of general type,
Math. Ann. 281 (1988), 123–133.
Google Scholar

[38]

S. T. Yau,
On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation,
Comm. Pure Appl. Math. 31 (1978), no. 3, 339–411.
Google Scholar

[39]

A. Zeriahi,
Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions,
Indiana Univ. Math. J. 50 (2001), 671–703.
Google Scholar

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