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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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Table of 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.