Comparison principles for Monge-Ampère measures on pluripolar sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917425839079424 |
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| author | Do, Thai Duong Pham, Hoang Hiep |
| author_facet | Do, Thai Duong Pham, Hoang Hiep |
| contents | In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the complex Monge--Ampère operator on pluripolar sets in the Cegrell classes. As applications, we obtain a characterization of this relation via auxiliary functions in the energy class and prove a corresponding uniqueness result for the Monge--Ampère equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparison principles for Monge-Ampère measures on pluripolar sets Do, Thai Duong Pham, Hoang Hiep Complex Variables 32W20, 32U15 In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the complex Monge--Ampère operator on pluripolar sets in the Cegrell classes. As applications, we obtain a characterization of this relation via auxiliary functions in the energy class and prove a corresponding uniqueness result for the Monge--Ampère equation. |
| title | Comparison principles for Monge-Ampère measures on pluripolar sets |
| topic | Complex Variables 32W20, 32U15 |
| url | https://arxiv.org/abs/2604.19347 |