Characterizing the range of the complex Monge-Ampère operator
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913761735999488 |
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| author | Liu, Songchen |
| author_facet | Liu, Songchen |
| contents | In this note, we solve the complex Monge-Ampère equation for measures with a pluripolar part in compact Kähler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Ampère operator in some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing the range of the complex Monge-Ampère operator Liu, Songchen Complex Variables Analysis of PDEs Differential Geometry 32W20, 32U15, 32Q15, 35D30 In this note, we solve the complex Monge-Ampère equation for measures with a pluripolar part in compact Kähler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Ampère operator in some special cases. |
| title | Characterizing the range of the complex Monge-Ampère operator |
| topic | Complex Variables Analysis of PDEs Differential Geometry 32W20, 32U15, 32Q15, 35D30 |
| url | https://arxiv.org/abs/2412.03445 |