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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.12817 |
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| _version_ | 1866909713453547520 |
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| author | Zhang, Wei Zhou, Qi |
| author_facet | Zhang, Wei Zhou, Qi |
| contents | Following the authors' recent work \cite{Zhang-Zhou2025}, we further explore the convexity properties of solutions to the Dirichlet problem for the complex Monge-Ampère operator. In this paper, we establish the $\log$-concavity of solutions to the Dirichlet eigenvalue problem for the complex Monge-Ampère operator on bounded, smooth, strictly convex domain in $\mathbb{C}^2$. The key ingredients consist of the constant rank theorem and the deformation method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The log-concavity of eigenfunction to complex Monge-Ampère operator in $\mathbb{C}^2$ Zhang, Wei Zhou, Qi Analysis of PDEs 35B50, 32W20 Following the authors' recent work \cite{Zhang-Zhou2025}, we further explore the convexity properties of solutions to the Dirichlet problem for the complex Monge-Ampère operator. In this paper, we establish the $\log$-concavity of solutions to the Dirichlet eigenvalue problem for the complex Monge-Ampère operator on bounded, smooth, strictly convex domain in $\mathbb{C}^2$. The key ingredients consist of the constant rank theorem and the deformation method. |
| title | The log-concavity of eigenfunction to complex Monge-Ampère operator in $\mathbb{C}^2$ |
| topic | Analysis of PDEs 35B50, 32W20 |
| url | https://arxiv.org/abs/2505.12817 |