| Title | Partial harmonicity of continuous maximal plurisubharmonic functions |
| Authors | Frank Wikström |
| Alternative Location | http://dx.doi.org/10.1080/0..., Restricted Access |
| Publication | Complex Variables and Elliptic Equations |
| Year | 2002 |
| Volume | 47 |
| Issue | 1 |
| Pages | 73 - 79 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Taylor & Francis |
| Abstract English | 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. |
| Keywords | Maximal Plurisubharmonic Functions, Positive Currents, Polynomial Hulls, |
| ISBN/ISSN/Other | ISSN: 1747-6933 (paper) |
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