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Partial harmonicity of continuous maximal plurisubharmonic functions

Wikström, Frank LU (2002) In Complex Variables and Elliptic Equations 47(1). p.73-79
Abstract
If u is a sufficiently smooth maximal plurisubharmonic function such that the complex Hessian of u has constant rank, it is known that there exists a foliation by complex manifolds, such that u is harmonic along the leaves of the foliation. In this paper, we show a partial analogue of this result for maximal plurisubharmonic functions that are merely continuous, without the assumption on the complex Hessian. In this setting, we cannot expect a foliation by complex manifolds, but we prove the existence of positive currents of bidimension (1, 1) such that the function is harmonic along the currents.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Maximal Plurisubharmonic Functions, Positive Currents, Polynomial Hulls
in
Complex Variables and Elliptic Equations
volume
47
issue
1
pages
73 - 79
publisher
Taylor & Francis
ISSN
1747-6933
DOI
10.1080/02781070290003173
language
English
LU publication?
no
id
9d30ff06-c4f1-4d99-912f-dbf3d95df62f (old id 1314619)
date added to LUP
2009-05-19 13:17:04
date last changed
2017-01-13 13:32:13
@article{9d30ff06-c4f1-4d99-912f-dbf3d95df62f,
  abstract     = {If u is a sufficiently smooth maximal plurisubharmonic function such that the complex Hessian of u has constant rank, it is known that there exists a foliation by complex manifolds, such that u is harmonic along the leaves of the foliation. In this paper, we show a partial analogue of this result for maximal plurisubharmonic functions that are merely continuous, without the assumption on the complex Hessian. In this setting, we cannot expect a foliation by complex manifolds, but we prove the existence of positive currents of bidimension (1, 1) such that the function is harmonic along the currents.},
  author       = {Wikström, Frank},
  issn         = {1747-6933},
  keyword      = {Maximal Plurisubharmonic Functions,Positive Currents,Polynomial Hulls},
  language     = {eng},
  number       = {1},
  pages        = {73--79},
  publisher    = {Taylor & Francis},
  series       = {Complex Variables and Elliptic Equations},
  title        = {Partial harmonicity of continuous maximal plurisubharmonic functions},
  url          = {http://dx.doi.org/10.1080/02781070290003173},
  volume       = {47},
  year         = {2002},
}