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Regularity properties of the degenerate Monge-Ampère equations on compact Kähler manifolds. (English) Zbl 1218.35114

Summary: The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampére equations on compact Kähler manifolds.

MSC:

35J96 Monge-Ampère equations
35B65 Smoothness and regularity of solutions to PDEs

References:

[1] Aubin, T., Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, New York, 1998. · Zbl 0896.53003
[2] Cascini, P. and La Nave, G., Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties, preprint. arXiv: math.AG/0603064
[3] Demailly, J.-P., Regularization of closed positive currents and intersection theory, J. Alg. Geom., 1, 1992, 361–409. · Zbl 0777.32016
[4] Demailly, J.-P. and Kollár, J., Semicontinuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds, Ann. Ec. Norm. Sup., 34, 2001, 525–556. arXiv: math.AG/9910118 · Zbl 0994.32021
[5] Demailly, J.-P. and Păun M., Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. Math. (2), 159(3), 2004, 1247–1274. · Zbl 1064.32019 · doi:10.4007/annals.2004.159.1247
[6] Demailly, J.-P. and Pali, N., Degenerate complex Monge-Ampère equations over compact Kähler manifolds, preprint. arXiv: 07105109V2
[7] Eyssidieux, Ph., Guedj, V. and Zeriahi, A., Singular Kähler-Einstein metrics, J. Amer. Math. Soc., to appear. arXiv: math.AG/0603431
[8] Kolodziej, S., The complex Monge-Ampère equation, Acta Math., 180, 1998, 69–117. · Zbl 0913.35043 · doi:10.1007/BF02392879
[9] Kolodziej, S. and Tian, G., A uniform L estimate for complex Monge-Ampère equations, Math. Ann., 342(4), 2008, 773–787. arXiv: 0710.1144 · Zbl 1159.32022 · doi:10.1007/s00208-008-0256-x
[10] Siu, Y.-T., Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., 27, 1974, 53–156. · Zbl 0289.32003 · doi:10.1007/BF01389965
[11] Siu, Y.-T., Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein metrics, Birkhäuser Verlag, Basel, 1987. · Zbl 0631.53004
[12] Skoda, H., Sous-ensembles analytiques d’ordre fini ou infini dans \(\mathbb{C}\)n, Bull. Soc. Math. France, 100, 1972, 353–408. · Zbl 0246.32009
[13] Tian, G. and Zhang, Z., On the Kähler-Ricci flow of projective manifolds of general type, Chin. Ann. Math., 27B(2), 2006, 179–192. · Zbl 1102.53047
[14] Tsuji, H., Existence and degeneration of Kähler-Einstein metrics on minimal algebraic manifolds of general type, Math. Ann., 281(1), 1988, 123–133. · Zbl 0631.53051 · doi:10.1007/BF01449219
[15] Yau, S.-T., On the Ricci curvature of a complex Kähler manifold and the complex Monge-Ampère equation, Comm. Pure Appl. Math., 31, 1978, 339–411. · Zbl 0369.53059 · doi:10.1002/cpa.3160310304
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