Plurisubharmonicity of envelopes of disc functionals on manifolds
| dc.creator | Larusson, Finnur | |
| dc.creator | Sigurdsson, Ragnar | |
| dc.date | 2001-11-23 | |
| dc.date | 2002-01-24 | |
| dc.date.accessioned | 2026-07-07T04:44:45Z | |
| dc.date.available | 2026-07-07T04:44:45Z | |
| dc.description | 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. | |
| dc.description | A few minor changes made 24 January 2002 | |
| dc.identifier | https://arxiv.org/abs/math/0111251 | |
| dc.identifier | http://arxiv.org/abs/math/0111251 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62716 | |
| dc.subject | Complex Variables | |
| dc.subject | 32U05 | |
| dc.title | Plurisubharmonicity of envelopes of disc functionals on manifolds | |
| dc.type | text |