Pluricomplex Green functions and the Dirichlet problem for the complex Monge-Ampère operator

Michigan Mathematical Journal

Volumn 44, Issue 3, 1997, Pages 579-596

  Zeriahi, Ahmed ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008989282     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1029005789     Document Type: Article

References (42)

1. E. Bedford, Survey of pluri-potential theory, Several complex variables (Stockholm, 1987/1988), pp. 48-97. Princeton Univ. Press, Princeton, NJ, 1993.
2. E. Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), 1-44.
3. _, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40.
4. Z. Blocki, The complex Monge-Ampère operator in hyperconvex domains, Doctoral thesis. Jagiellonian Univ., Krakow, Poland, 1995.
5. H. Bremermann, On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Characterization of Šhilov boundaries, Trans. Amer. Math. Soc. 91 (1959), 246-276.
6. U. Cegrell, On the Dirichlet problem for the complex Monge-Ampère operator, Math. Z. 185 (1984), 247-251.
7. n, Math. Z. 193 (1986), 373-380.
8. _, Capacities in complex analysis, Aspects of Math., E14, Vieweg, Braunschweig, 1988.
9. U. Cegrell and S. Kolodziej, The Dirichlet problem for the complex Monge-Ampère operator: Perron classes and rotation invariant measures, Michigan Math. J. 41 (1994), 563-569.
10. 2, Michigan Math. J. 39 (1992), 145-151.
11. U. Cegrell and A. Sadullaev, Approximation of plurisubharmonic functions and the Dirichlet problem for the complex Monge-Ampère operator, Math. Scand, 71 (1992), 62-68.
12. J. P. Demailly, Mesures de Monge-Ampère et caractérisation des variété algébriques affines, Mém. Soc. Math. France (N.S.) 19 (1985), 1-125.
13. _, Mesures de Monge-Ampère et mesures pluriharmoniques, Math. Z. 194 (1987), 519-564.
14. _, Potential theory in several complex variables, ICPAM Summer School on Complex Analysis, Nice, France, 1989.
15. _, Regularization of closed positive currents and intersection theory, J. Algebraic Geom. 1 (1992), 361-409.
16. L. Hörmander, An introduction to complex analysis in several variables, 3rd. ed., North-Holland, New York, 1990.
17. M. Jarnicki and P. Pflug, Invariant distances and metrics in complex analysis, de Gruyter, Berlin, 1993.
18. N. Kerzman and J. P. Rosay, Fonctions plurisousharmoniques d'exhaustion bornées et domaines taut, Math. Ann. 257 (1981), 171-184.
19. C. O. Kiselman, Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107 (1979), 295-304.
20. _, Attenuating the singularities of plurisubharmonic functions, Ann. Polon. Math. 60 (1994), 173-197.
21. M. Klimek, Extremal plurisubharmonic functions and invariant pseudodistances, Bull. Soc. Math. France 113 (1985), 231-240.
22. _, Pluripotential theory, Oxford University Press, New York, 1991.
23. _, Invariant pluricomplex Green functions, Topics in complex analysis, vol. 31, pp. 207-226, Banach Center Publications, Institut of Mathematics, Polish Academy of Sciences, Warsaw, 1995.
24. S. Kolodziej, The range of the complex Monge-Ampère operator, Indiana Univ. Math. J. 43 (1994), 1321-1338.
25. _, The range of the complex Monge-Ampère operator II. Indiana Univ. Math. J. 44 (1995), 765-782.
26. _, The complex Monge-Ampère equation, preprint, Institut of Math, of Jagielonski Univ., Krakow, Poland, 1995.
27. _, Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator, Ann. Polon. Math. 65 (1996), 11-21.
28. P. Lelong, Fonctions plurisousharmoniques et formes différentielle positives, Gordon & Breach, New York / Dunod, Paris, 1968.
29. _, Fonction de Green pluricomplexe et lemmes de Schwarz dans les espaces de Banach, J. Math. Pures Appl. (9) 68 (1989), 319-347.
30. L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474.
31. _, Solving the degenerate Monge-Ampère equation with one concentrated singularity, Math. Ann. 263 (1983), 515-532.
32. n, Indiana Univ. Math. J. 44 (1995), 489-510.
33. L. Persson, On the Dirichlet problem for the complex Monge-Ampère operator, Thesis, Univ. of Umea, 1992.
34. E. A. Poletsky, Holomorphic currents, Indiana Univ. Math. J. 42 (1993), 85-144.
35. N. Sibony, Quelques problèmes de prolongement de courants en analyse complexe, Duke Math. J. 52 (1985), 157-197.
36. _, Une classe de domaines pseudoconvexes, Duke Math. J. 55 (1987), 299-319.
37. Y. T. Siu, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1974), 53-156.
38. J. L. Stehlé, Fonctions plurisousharmoniques et convexité holomorphe de certains fibrés analytiques, Séminaire P. Lelong, Lecture Notes in Math., 474, pp. 155-179, Springer, Berlin, 1975.
39. M. Tsuji, Potential theory in modern function theory, Chelsa, New York, 1975.
40. V. P. Zahariuta, Spaces of analytic functions and complex potential theory, Linear Topol. Spaces Complex Anal. 1 (1994), 74-146.
41. A. Zeriahi, Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes, Ann. Polon. Math. 50 (1989), 81-91.
42. _, Pluricomplex Green functions and approximation of holomorphic functions, Complex analysis, harmonic analysis and applications, Pitman Res. Math. Notes Ser., 347, pp. 104-142, Longman, Harlow, U.K., 1996.