Partial harmonicity of continuous maximal plurisubharmonic functions
(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:
https://lup.lub.lu.se/record/1314619
- author
- Wikström, Frank LU
- publishing date
- 2002
- 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}}, }