Partial harmonicity of continuous maximal plurisubharmonic functions

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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.
Originalspråkengelska
Sidor (från-till)73-79
TidskriftComplex Variables and Elliptic Equations
Volym47
Nummer1
DOI
StatusPublished - 2002
Externt publiceradJa

Ämnesklassifikation (UKÄ)

  • Matematik
  • Matematisk analys

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