发表机构
Institute for Artificial Intelligence, VNU University of Engineering and Technology; Department of Mathematics, National University of Singapore（越南国立大学工程技术大学人工智能研究所; 新加坡国立大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了复流形上Cegrell类局部多重次调和势的加权比较原理，并应用于$\mathbb C^2$中具有特定奇异性的函数，得出极大性等价于Monge-Ampère测度消失且为局部性质。
AI 中文摘要
我们证明了在任意复流形上，在适当的边界和粘合条件下，Cegrell类中局部多重次调和势的一个加权比较原理。当流形具有一个全局多重次调和函数（属于$\mathcal E_{\mathrm{loc}}$），其Monge-Ampère测度的绝对连续部分几乎处处具有正密度时，我们得到了支配性和唯一性。我们将这些结果应用于$\mathbb C^2$中域上的多重次调和函数，这些函数的奇异性满足涉及$\alpha\log\\|f\\|$和Cegrell势的局部不等式。对于此类函数，极大性等价于减去Siu除子部分后剩余电流的Monge-Ampère测度消失。因此，极大性在此类中是局部性质。
英文摘要
We prove a weighted comparison principle for local plurisubharmonic potentials in Cegrell's class on an arbitrary complex manifold under suitable boundary and gluing conditions. We obtain domination and uniqueness when the manifold admits a global psh function in $\mathcal E_{\mathrm{loc}}$ whose Monge-Ampère measure has an absolutely continuous part with positive density almost everywhere. We apply these results to plurisubharmonic functions on domains in $\mathbb C^2$ whose singularities satisfy local inequalities involving $α\log\|f\|$ and a Cegrell potential. For such functions, maximality is equivalent to the vanishing of the Monge-Ampère measure of the current remaining after subtraction of the Siu divisorial part. Consequently, maximality is a local property in this class.
