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The Dirichlet problem for a complex Monge-Ampere equation
Author(s):
Eric
Bedford;
B. A.
Taylor
Journal:
Bull. Amer. Math. Soc.
82
(1976),
102-104.
MSC (1970):
Primary 32F05, 35D05;
Secondary 32E99
MathSciNet review:
0393574
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Additional information
References:
- 1.
- A. D. Alexandrov, Dirichlet's problem for the equation ${\rm Det}\,\vert\vert z\sbij\vert\vert =\varphi (z\sb{1},\cdots,z\sbn,z, x\sb{1},\cdots, x\sbn)$. I., Vestnik Leningrad Univ. Ser. Mat. Meh. Astr. 13 (1958), no. 1, 5-24. (Russian) MR 20 #3385. MR 96903
- 2.
- H. J. Bremermann, On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains. Characterization of Šilov boundaries, Trans. Amer. Math. Soc. 91 (1959), 246-276. MR 25 #227. MR 136766
- 3.
- S. S. Chern, Harold I. Levine and L. Nirenberg, Intrinsic norms on a complex manifold, Global Analysis (Papers in honor of K. Kodaira), Univ. of Tokyo Press, Tokyo, 1969, pp. 119-139. MR 254877
- 4.
- P. Lelong, Fonctions plurisousharmoniques et formed différentielles positives, Gordon and Breach, New York, 1968. MR 39 #4436. MR 243112
- 5.
- A. V. Pogorelov, Monge-Ampere equations of elliptic type, Izdat. Har'kovsk. Univ., Kharkov, 1960; English transl., Noordhoff, Groningen, 1964. MR 23 #A1137; 31 #4993. MR 180763
- 6.
- A. V. Pogorelov, The Dirichlet problem for the n-dimensional analogue of the Monge-Ampere equation, Dokl. Akad. Nauk SSSR 201 (1971), 790-793 = Soviet Math. Dokl. 12 (1971), 1727-1731. MR 45 #2305. MR 293228
- 7.
- Y. T. Siu, Extension of meromorphic maps, Ann. of Math. (to appear).
- 8.
- J. B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech. 18 (1968/69), 143-148. MR 37 #3049. MR 227465
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Additional Information:
DOI:
10.1090/S0002-9904-1976-13977-8
PII:
S 0002-9904(1976)13977-8
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