The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Ampère flow with a general measure on the right-hand side
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916616756789248 |
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| author | Kang, Bowoo |
| author_facet | Kang, Bowoo |
| contents | We show that the pluripotential Cauchy-Dirichlet problem for the complex Monge-Ampère flow is solvable 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. In particular, we remove the strict positivity assumption on $dμ$. We use this result to prove the parabolic version of the bounded subsolution theorem due to Kolodziej in pluripotential theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Ampère flow with a general measure on the right-hand side Kang, Bowoo Complex Variables We show that the pluripotential Cauchy-Dirichlet problem for the complex Monge-Ampère flow is solvable 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. In particular, we remove the strict positivity assumption on $dμ$. We use this result to prove the parabolic version of the bounded subsolution theorem due to Kolodziej in pluripotential theory. |
| title | The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Ampère flow with a general measure on the right-hand side |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2501.16765 |