Plurisubharmonicity of envelopes of disc functionals on manifolds
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Bibliographic record
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.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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