Plurisubharmonicity of envelopes of disc functional on manifolds

Finnur Lárusson*, Ragnar Sigurdsson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We show that a disc functional on a complex manifold has a plurisubharmonic envelope if all its pullbacks by holomorphic submersions from domains of holomorphy in affine space do and it is locally bounded above and upper semicontinuous in a certain weak sense. For naturally defined classes of disc functionals on manifolds, this result reduces a property somewhat stronger than having a plurisubharmonic envelope to the affine case. The proof uses a recent Stein neighbourhood construction of Rosay, who proved the plurisubharmonicity of the Poisson envelope on all manifolds. As a consequence, the Riesz envelope and the Lelong envelope are plurisubharmonic on all manifolds; for the former, we make use of new work of Edigarian. The basic theory of the three main classes of disc functionals is thereby extended to all manifolds.

Original languageEnglish
Pages (from-to)27-38
Number of pages12
JournalJournal fur die Reine und Angewandte Mathematik
Issue number555
Publication statusPublished - 2003

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