论文标题
打击 - liouville方程和准的解决方案 - 正常
Blow--up Solutions of Liouville's Equation and Quasi--Normality
论文作者
论文摘要
我们证明，所有Meromorormormormorthic函数的$ \ Mathcal {f} _C（d）$在一个域上$ d \ subseteq \ subseteq \ mathbb {c} $与图像域$ f（d）$的球形区域的属性均匀地限制了$ cou2 $ cou2 $ is quasi is quasi $ normal of dep $ c $ cus $ cus $ cus $ cus $ cus $ c $ cy $ cy $ cus--normal cus y rede。我们还讨论了这一结果与Liouville方程式解决方案的井（Brézis和Merle的著名作品）之间的密切关系。这些结果完全符合格罗莫夫的紧凑定理的精神，正如本文结尾所指出的那样。
We prove that the family $\mathcal{F}_C(D)$ of all meromorphic functions $f$ on a domain $D\subseteq \mathbb{C}$ with the property that the spherical area of the image domain $f(D)$ is uniformly bounded by $C π$ is quasi--normal of order $\le C$. We also discuss the close relations between this result and the well--known work of Brézis and Merle on blow--up solutions of Liouville's equation. These results are completely in the spirit of Gromov's compactness theorem, as pointed out at the end of the paper.
