论文标题
Fridman功能，注入性半径功能和挤压功能
Fridman Function, Injectivity Radius Function and Squeezing Function
论文作者
论文摘要
最近，复杂的歧管$ x $的Fridman功能已被确定为$ x $的挤压功能的双重功能。在本文中，我们证明了某些双曲复合歧管$ x $的Fridman功能在上面的$ x $的Injextitive Radius函数上面界定。该结果还建议我们使用Fridman函数将均匀厚度的定义扩展到高维双曲复合歧管上。当$ x = \ mathbb {d} \ diagupγ$和$γ$是标准开放单位磁盘$ \ mathbb {d} $时，我们还为弗里德曼函数（相对于Kobayashi度量）建立了一个表达式（相对于Kobayashi度量）。因此，fridman函数的明确公式和刺穿的磁盘$ \ mathbb {d}^*$得出了。这些是第一个显式的非恒定弗里德曼功能。最后，我们分别探讨了弗里德曼函数的边界行为（相对于Kobayashi公制），并分别针对常规类型双曲线Riemann表面和平面域的挤压功能。
Very recently, the Fridman function of a complex manifold $X$ has been identified as a dual of the squeezing function of $X$. In this paper, we prove that the Fridman function for certain hyperbolic complex manifold $X$ is bounded above by the injectivity radius function of $X$. This result also suggests us to use the Fridman function to extend the definition of uniform thickness to higher-dimensional hyperbolic complex manifolds. We also establish an expression for the Fridman function (with respect to the Kobayashi metric) when $X = \mathbb{D} \diagup Γ$ and $Γ$ is a torsion-free discrete subgroup of isometries on the standard open unit disk $\mathbb{D}$. Hence, explicit formulae of the Fridman functions for the annulus $A_r$ and the punctured disk $\mathbb{D}^*$ are derived. These are the first explicit non-constant Fridman functions. Finally, we explore the boundary behaviour of the Fridman functions (with respect to the Kobayashi metric) and the squeezing functions for regular type hyperbolic Riemann surfaces and planar domains respectively.
