论文标题
在有限连接的平面域的挤压功能上
On the squeezing function for finitely connected planar domains
论文作者
论文摘要
在最近的一篇论文中，NG，Tang和Tsai（Math。Ann。2020）发现了通过Loewner微分方程的Annulus挤压功能的明确公式。他们的结果使他们猜想了任何有限连接性的平面域的相应公式，表明挤压功能问题中的极值是针对适当选择的共形映射到圆形狭缝磁盘上的。在本文中，我们反驳了这个猜想。我们还提供了概念上简单的潜在理论证明，以证明对环的挤压功能的显式公式，该公式具有识别所有极端功能的额外优势。
In a recent paper, Ng, Tang and Tsai (Math. Ann. 2020) have found an explicit formula for the squeezing function of an annulus via the Loewner differential equation. Their result has led them to conjecture a corresponding formula for planar domains of any finite connectivity stating that the extremum in the squeezing function problem is achieved for a suitably chosen conformal mapping onto a circularly slit disk. In this paper we disprove this conjecture. We also give a conceptually simple potential-theoretic proof of the explicit formula for the squeezing function of an annulus which has the added advantage of identifying all extremal functions.
