Geometry of Kähler metrics and foliations by holomorphic discs
Publications Mathématiques de l'IHÉS, Tome 107 (2008), pp. 1-107. 
@article{PMIHES_2008__107__1_0,
     author = {Chen, X. X. and Tian, G.},
     title = {Geometry of {K\"ahler} metrics and foliations by holomorphic discs},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--107},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {107},
     year = {2008},
     doi = {10.1007/s10240-008-0013-4},
     mrnumber = {2434691},
     zbl = {1182.32009},
     language = {en},
     url = {http://www.numdam.org/articles/10.1007/s10240-008-0013-4/}
}
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Chen, X. X.; Tian, G. Geometry of Kähler metrics and foliations by holomorphic discs. Publications Mathématiques de l'IHÉS, Tome 107 (2008), pp. 1-107. doi : 10.1007/s10240-008-0013-4. http://www.numdam.org/articles/10.1007/s10240-008-0013-4/

[1] Bando, S., Mabuchi, T. (1987) Uniqueness of Einstein Kähler metrics modulo connected group actions. Algebr. Geom., Sendai, 1985, Adv. Stud. Pure Math. 10: pp. 11-40 | MR | Zbl

[2] Bedford, E.D., Taylor, T.A. (1976) The Dirichlet problem for the complex Monge-Ampere operator. Invent. Math. 37: pp. 1-44 | MR | Zbl

[3] Calabi, E. (1957) An extension of e. Hopf's maximum principle with an application to Riemannian geometry. Duke Math. J. 25: pp. 45-56 | MR | Zbl

[4] Calabi, E. (1982) Extremal Kähler metrics. Seminar on Differential Geometry. Princeton University Press, Princeton, pp. 259-290 | MR | Zbl

[5] Calabi, E. (1985) Extremal Kähler metrics. II. Differential Geometry and Complex Analysis. Springer, Berlin, pp. 95-114 | MR | Zbl

[6] Calabi, E., Chen, X.X. (2002) The space of Kähler metrics. II. J. Differ. Geom. 61: pp. 173-193 | MR | Zbl

[7] Chen, X.X. (1998) Extremal Hermitian metrics in Riemann surface. Int. Math. Res. Not. 15: pp. 781-797 | MR | Zbl

[8] Chen, X.X. (2000) On the lower bound of the Mabuchi energy and its application. Int. Math. Res. Not. 2000: pp. 607-623 | MR | Zbl

[9] Chen, X.X. (2000) Space of Kähler metrics. J. Differ. Geom. 56: pp. 189-234 | MR | Zbl

[10] Cohen, R.L., Lupercio, E., Segal, G.B. (2000) Holomorphic spheres in loop groups and Bott periodicity. Surveys in Differential Geometry. Int. Press, Somerville, MA, pp. 83-106 | MR | Zbl

[11] Donaldson, S.K. (1999) Symmetric spaces, Kähler geometry and Hamiltonian dynamics, Northern California Symplectic Geometry Seminar. Amer. Math. Soc. Transl. 196: pp. 13-33 | MR | Zbl

[12] Donaldson, S.K. (2001) Holomorphic discs and the complex Monge-Ampère equation. J. Sympletic Geom. 1: pp. 171-196 | MR | Zbl

[13] Donaldson, S.K. (2005) Scalar curvature and projective embeddings, II. Q. J. Math. 56: pp. 345-356 | MR | Zbl

[14] Fostneric, F. (1987) Analytic discs with boundaries in a maximal real submanifolds of ℂ 2 . Ann. Inst. Fourier 37: pp. 1-44 | Numdam | MR | Zbl

[15] Futaki, A. (1992) Remarks on extremal Kähler metrics on ruled manifolds. Nagoya Math. J. 126: pp. 89-101 | MR | Zbl

[16] Globenik, J. (1994) Perturbation by analytic discs along maximal real submanifolds of ℂ n . Math. Z. 217: pp. 287-316 | MR | Zbl

[17] Nirenberg, L., Caffarelli, L., Spruck, J. (1984) The Dirichlet problem for nonlinear second-order elliptic equation I, Monge-Ampere equation. Comm. Pure Appl. Math. 37: pp. 369-402 | MR | Zbl

[18] Kohn, J.T., Nirenberg, L., Caffarelli, L., Spruck, J. (1985) The Dirichlet problem for nonlinear second-order elliptic equation II. Complex Monge-Ampere equation. Comm. Pure Appl. Math. 38: pp. 209-252 | MR | Zbl

[19] Lempert, L. (1983) Solving the degenerate Monge-Ampere equation with one concentrated singularity. Math. Ann. 263: pp. 515-532 | MR | Zbl

[20] Mabuchi, T. (1987) Some symplectic geometry on compact Kähler manifolds I. Osaka J. Math. 24: pp. 227-252 | MR | Zbl

[21] Oh, Y.G. (1995) Riemann-Hilbert problem and application to the perturbation theory of analytic discs. Kyungpook Math. J. 35: pp. 38-75 | MR | Zbl

[22] Oh, Y.G. (1996) Fredhom theory of holomorphic discs under the perturbation theory of boundary conditions. Math. Z. 222: pp. 505-520 | MR | Zbl

[23] Osserman, R. (1957) On the inequality Δu≥f(u). Pac. J. Math. 7: pp. 1641-1647 | MR | Zbl

[24] S. Paul and G. Tian, Algebraic and analytic K-stability, preprint, math/0404223.

[25] Semmes, S. (1992) Complex Monge-Ampère equations and sympletic manifolds. Amer. J. Math. 114: pp. 495-550 | MR | Zbl

[26] Tian, G. (1990) On Calabi's conjecture for complex surfaces with positive first Chern class. Invent. Math. 101: pp. 101-172 | MR | Zbl

[27] Tian, G. (1997) Kähler-Einstein metrics with positive scalar curvature. Invent. Math. 130: pp. 1-39 | MR | Zbl

[28] Tian, G. (2000) Canonical Metrics in Kähler Geometry (Notes taken by Meike Akveld). Birkhäuser, Basel | MR | Zbl

[29] Tian, G. (2000) Bott-Chern forms and geometric stability. Discrete Contin. Dyn. Syst. 6: pp. 211-220 | MR | Zbl

[30] Tian, G., Zhu, X.H. (2002) A new holomorphic invariant and uniqueness of Kähler-Ricci solitons. Comment. Math. Helv. 77: pp. 297-325 | MR | Zbl

[31] Vekuba, N.P. (1967) Systems of Singular Integral Equations. Groningen, Nordhoff

[32] Yau, S.T. (1978) On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation, I*. Comm. Pure Appl. Math. 31: pp. 339-441 | MR | Zbl

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