Sammanfattning
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.
Originalspråk | engelska |
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Sidor (från-till) | 73-79 |
Tidskrift | Complex Variables and Elliptic Equations |
Volym | 47 |
Nummer | 1 |
DOI | |
Status | Published - 2002 |
Externt publicerad | Ja |
Ämnesklassifikation (UKÄ)
- Matematik
- Matematisk analys