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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.
Please use this url to cite or link to this publication:
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
2016-04-01 12:09:13
date last changed
2018-11-21 20:04:23
@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}},
  keywords     = {{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}},
  doi          = {{10.1080/02781070290003173}},
  volume       = {{47}},
  year         = {{2002}},
}