On a conjecture of Hunt and Murray concerning $q$-plurisubharmonic functions
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- by Morris Kalka PDF
- Proc. Amer. Math. Soc. 73 (1979), 30-34 Request permission
Abstract:
We discuss the conjecture of Hunt and Murray on uniqueness of the Dirichlet problem for the generalized complex Monge-Ampère equation. We define a class of q-plurisubharmonic functions, prove uniqueness in this class, and show that in some cases the solution found by Hunt and Murray is in our class.References
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E. Bedford and D. Burns, Holomorphic mappings of annuli in ${{\mathbf {C}}^n}$ and the associated extremal function, preprint.
- Eric Bedford and Morris Kalka, Foliations and complex Monge-Ampère equations, Comm. Pure Appl. Math. 30 (1977), no. 5, 543–571. MR 481107, DOI 10.1002/cpa.3160300503
- 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 136766, DOI 10.1090/S0002-9947-1959-0136766-9
- L. R. Hunt and John J. Murray, $q$-plurisubharmonic functions and a generalized Dirichlet problem, Michigan Math. J. 25 (1978), no. 3, 299–316. MR 512901
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 30-34
- MSC: Primary 32F05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0512052-8
- MathSciNet review: 512052