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Partial harmonicity of continuous maximal plurisubharmonic functions

In English

Författare

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.

Publiceringsår

2002

Språk

Engelska

Sidor

73-79

Publikation/Tidskrift/Serie

Complex Variables and Elliptic Equations

Volym

47

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

Taylor & Francis

Ämne

  • Mathematics
  • Mathematical Analysis

Nyckelord

  • Maximal Plurisubharmonic Functions
  • Positive Currents
  • Polynomial Hulls

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 1747-6933