复 Monge-Ampère 方程在 $\mathbb{C}^2$ 中解的幂凸性
偏微分方程分析
2025-08-01 v2
摘要
边界值问题中解的凸性（如实或复 次 Hessian 方程）是一难题。本文在 中具有光滑、严格凸域的复 Monge-Ampère 方程 Dirichlet 问题解的幂凸性问题得到建立。我们的ethods 基于常数秩定理与变形过程。
引用
@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}
}
备注
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