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Partial harmonicity of continuous maximal plurisubharmonic functions

På svenska

Author

Summary, in 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.

Publishing year

2002

Language

English

Pages

73-79

Publication/Series

Complex Variables and Elliptic Equations

Volume

47

Issue

1

Document type

Journal article

Publisher

Taylor & Francis

Topic

  • Mathematics
  • Mathematical Analysis

Keywords

  • Maximal Plurisubharmonic Functions
  • Positive Currents
  • Polynomial Hulls

Status

Published

ISBN/ISSN/Other

  • ISSN: 1747-6933