Bordered complex Hessians

John P. D'Angelo

Research output: Contribution to journalArticle

Abstract

We record some basic facts about bordered complex Hessians and logarithmically plurisubharmonic functions. These enable us to prove that a nonnegative bihomogeneous polynomial is plurisubharmonic if and only if it is log-plurisubharmonic; we give a more general version for twice differentiable bihomogeneous functions. The proof relies on the vanishing of the determinant of the bordered complex Hessian; we go on to find general classes of solutions to the nonlinear PDE given by setting the determinant of a bordered complex Hessian equal to zero.

Original languageEnglish (US)
Pages (from-to)561-571
Number of pages11
JournalJournal of Geometric Analysis
Volume11
Issue number4
StatePublished - Jan 1 2001

Keywords

  • Bihomogeneous polynomial
  • Bordered complex Hessian
  • Log-plurisubharmonic
  • Plurisubharmonic

ASJC Scopus subject areas

  • Geometry and Topology

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  • Cite this

    D'Angelo, J. P. (2001). Bordered complex Hessians. Journal of Geometric Analysis, 11(4), 561-571.