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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/2505.11002 |
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| _version_ | 1866912512662831104 |
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| author | Zhang, Wei Zhou, Qi |
| author_facet | Zhang, Wei Zhou, Qi |
| contents | The convexity of solutions to boundary value problems for fully nonlinear elliptic partial differential equations (such as real or complex $k$-Hessian equations) is a challenging topic. In this paper, we establish the power convexity of solutions to the Dirichlet problem for the complex Monge-Ampère equation on bounded, smooth, strictly convex domain in $\mathbb{C}^2$. Our approach is based on the constant rank theorem and the deformation process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power convexity of solutions to complex Monge-Ampère equation in $\mathbb{C}^2$ Zhang, Wei Zhou, Qi Analysis of PDEs 35B50, 32W20 The convexity of solutions to boundary value problems for fully nonlinear elliptic partial differential equations (such as real or complex $k$-Hessian equations) is a challenging topic. In this paper, we establish the power convexity of solutions to the Dirichlet problem for the complex Monge-Ampère equation on bounded, smooth, strictly convex domain in $\mathbb{C}^2$. Our approach is based on the constant rank theorem and the deformation process. |
| title | Power convexity of solutions to complex Monge-Ampère equation in $\mathbb{C}^2$ |
| topic | Analysis of PDEs 35B50, 32W20 |
| url | https://arxiv.org/abs/2505.11002 |