A general comparison principle for the pluripotential complex Monge-Ampère flow
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915674205454336 |
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| author | Kang, Bowoo |
| author_facet | Kang, Bowoo |
| contents | We prove a comparison principle for the pluripotential complex Monge-Ampère flows for the right-hand side of the form $dt \wedge dμ$ where $dμ$ is dominated by a Monge-Ampère measure of a bounded plurisubharmonic function. As a consequence, we obtain the uniqueness of the weak solution to the pluripotential Cauchy-Dirichlet problem. We also study the long-term behavior of the solution under some assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A general comparison principle for the pluripotential complex Monge-Ampère flow Kang, Bowoo Complex Variables Analysis of PDEs Differential Geometry We prove a comparison principle for the pluripotential complex Monge-Ampère flows for the right-hand side of the form $dt \wedge dμ$ where $dμ$ is dominated by a Monge-Ampère measure of a bounded plurisubharmonic function. As a consequence, we obtain the uniqueness of the weak solution to the pluripotential Cauchy-Dirichlet problem. We also study the long-term behavior of the solution under some assumption. |
| title | A general comparison principle for the pluripotential complex Monge-Ampère flow |
| topic | Complex Variables Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2511.06412 |