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Complex Monge-Ampère of a maximum

Author(s): Eric Bedford; Sione Ma'u
Journal: Proc. Amer. Math. Soc. 136 (2008), 95-101.
MSC (2000): Primary 32U40, 32W20; Secondary 58C35
Posted: October 16, 2007
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Abstract: We derive a formula for $(dd^{c}u)^{n}$ where $u=\max _{j}u_{j}$ is a finite maximum. As an application, we compute the complex equilibrium measures of some generalized polyhedra.

References:

[1]: E. Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), no. 1, 1-44. MR 0445006 (56:3351)
[2]: Z. B $\l$ ocki, Equilibrium measure of a product set of ${\mathbb{C}}^{n}$ , Proc. A.M.S. 128 (2000), no. 12, 3595-3599. MR 1707508 (2001b:32072)
[3]: -, The domain of definition of the complex Monge-Ampère operator, Amer. J. Math. 128 (2006), no. 2, 519-530. MR 2214901 (2006k:32076)
[4]: S. Ma`u, Plurisubharmonic Functions of Logarithmic Growth, PhD Thesis, University of Auckland, Auckland, New Zealand, 2003.

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Additional Information:

Eric Bedford
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: bedford@indiana.edu

Sione Ma'u
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: sinmau@indiana.edu

DOI: 10.1090/S0002-9939-07-09145-9
PII: S 0002-9939(07)09145-9
Keywords: Current, measure, Monge-Amp\`{e}re, plurisubharmonic
Received by editor(s): June 9, 2006
Posted: October 16, 2007
Additional Notes: The first author was supported in part by the NSF
The second author was supported by a New Zealand Science and Technology Post-Doctoral fellowship, contract no. IDNA0401.
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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