Hermitian 流形上 $(n-1)$-PSH 函数的 Monge-Ampère 方程 Dirichlet 问题
偏微分方程分析
2022-03-15 v1 微分几何
摘要
我们通过推导在 -PSH 次解假设下的边界估计的定量版本，解决了右端可能退化的 -PSH 函数的 Monge-Ampère 方程 Dirichlet 问题。此外，我们在带边界的紧 Riemann 曲面与闭平衡流形的乘积上确认了次解假设。
引用
@article{arxiv.2203.07232,
title = {The Dirichlet problem for Monge-Amp\`ere equation for $(n-1)$-PSH functions on Hermitian manifolds},
author = {Rirong Yuan},
journal= {arXiv preprint arXiv:2203.07232},
year = {2022}
}
备注
The main context of this paper is the integration of the second parts of [arXiv:2001.09238] and [arXiv:2106.14837], while [arXiv: 2203.03439], and the first parts of [arXiv:2001.09238] and [arXiv:2106.14837] are reorganized into a separate paper [arXiv:2203.04898]. More precisely, this paper is essentially extracted from Section 7 in [arXiv:2001.09238] and Section 4 in [arXiv:2106.14837]