亚纯拟双列体的特征
Characterizing meromorphic pseudo-lemniscates
摘要：
设$f$是具有单连通区域$G\subset\mathbb{C}$的亚纯函数，$Γ\subset\mathbb{C}$是光滑Jordan曲线.我们将$G$中的$f^{-1}(Γ)$组件称为$f$的$Γ$ - $pseudo$- $lemniscate$。本文给出了$G$中的光滑Jordan曲线$\mathcal{S}$（具有有界面$D$）是$f$的伪双纽线的判别准则，该判别准则是由给定的$w$在$D$中的$f$下的原像数（以重数计算）给出的，因为$w$的范围在黎曼球面上.我们还开发了一个测试，在相同的条件下，其中一个可以显示的图像下的约旦曲线$f$是不是约旦曲线。
英文摘要：
Let $f$ be a meromorphic function with simply connected domain $G\subset\mathbb{C}$, and let $Γ\subset\mathbb{C}$ be a smooth Jordan curve. We call a component of $f^{-1}(Γ)$ in $G$ a $Γ$-$pseudo$-$lemniscate$ of $f$. In this note we give criteria for a smooth Jordan curve $\mathcal{S}$ in $G$ (with bounded face $D$) to be a psuedo-lemniscate of $f$ in terms of the number of preimages (counted with multiplicity) which a given $w$ has under $f$ in $D$, as $w$ ranges over the Riemann sphere. We also develop a test, in the same terms, by which one may show that the image of a Jordan curve under $f$ is not a Jordan curve.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
