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Complex Monge-Ampère of a maximum
Authors:
Eric Bedford and Sione Ma'u
Journal:
Proc. Amer. Math. Soc. 136 (2008), 95-101
MSC (2000):
Primary 32U40, 32W20; Secondary 58C35
Posted:
October 16, 2007
MathSciNet review:
2350393
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Additional Information
Abstract: We derive a formula for  where  is a finite maximum. As an application, we compute the complex equilibrium measures of some generalized polyhedra.
- [1]
Eric
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]
Zbigniew
Błocki, Equilibrium measure of a product
subset of 𝐶ⁿ, Proc. Amer. Math.
Soc. 128 (2000), no. 12, 3595–3599. MR 1707508
(2001b:32072), http://dx.doi.org/10.1090/S0002-9939-00-05552-0
- [3]
Zbigniew
Błocki, 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.
- [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
 ocki, Equilibrium measure of a product set of  , 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:
http://dx.doi.org/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
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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