$m$-Positivity and Regularisation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918177876738048 |
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| author | Dinew, Sławomir Popovici, Dan |
| author_facet | Dinew, Sławomir Popovici, Dan |
| contents | Starting from the notion of $m$-plurisubharmonic function introduced recently by Dieu and studied, in particular, by Harvey and Lawson, we consider $m$-(semi-)positive $(1,\,1)$-currents and Hermitian holomorphic line bundles on complex Hermitian manifolds and prove two kinds of results: vanishing theorems and $L^2$-estimates for the $\bar\partial$-equation in the context of $C^\infty$ $m$-positive Hermitian fibre metrics; global and local regularisation theorems for $m$-semi-positive $(1,\,1)$-currents whose proofs involve the use of viscosity subsolutions for a certain Monge-Ampère-type equation and the associated Dirichlet problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $m$-Positivity and Regularisation Dinew, Sławomir Popovici, Dan Differential Geometry Algebraic Geometry Complex Variables Starting from the notion of $m$-plurisubharmonic function introduced recently by Dieu and studied, in particular, by Harvey and Lawson, we consider $m$-(semi-)positive $(1,\,1)$-currents and Hermitian holomorphic line bundles on complex Hermitian manifolds and prove two kinds of results: vanishing theorems and $L^2$-estimates for the $\bar\partial$-equation in the context of $C^\infty$ $m$-positive Hermitian fibre metrics; global and local regularisation theorems for $m$-semi-positive $(1,\,1)$-currents whose proofs involve the use of viscosity subsolutions for a certain Monge-Ampère-type equation and the associated Dirichlet problem. |
| title | $m$-Positivity and Regularisation |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2510.25639 |