Power convexity of solutions to complex Monge-Amp\`ere equation in $\mathbb{C}^2$
Analysis of PDEs
2025-08-01 v2
Abstract
The convexity of solutions to boundary value problems for fully nonlinear elliptic partial differential equations (such as real or complex -Hessian equations) is a challenging topic. In this paper, we establish the power convexity of solutions to the Dirichlet problem for the complex Monge-Amp\`ere equation on bounded, smooth, strictly convex domain in . Our approach is based on the constant rank theorem and the deformation process.
Keywords
Cite
@article{arxiv.2505.11002,
title = {Power convexity of solutions to complex Monge-Amp\`ere equation in $\mathbb{C}^2$},
author = {Wei Zhang and Qi Zhou},
journal= {arXiv preprint arXiv:2505.11002},
year = {2025}
}
Comments
The proof of the constant rank theorem in this paper (Section 3) is incomplete. Therefore, we are withdrawing the submission. A revised version will be uploaded once the issue has been corrected