AI 中文总结
本文在Avkhadiev--Wirths几何框架下，通过显式超越方程刻画了与指数映射相关的单叶函数类的凹性半径，构造极值函数证明全局尖锐性，并数值验证了半径关于参数A的严格单调性。
AI 中文摘要
我们确定了与指数映射 $e^z$ 相关的单叶函数类 $\mathcal{S}_e^*$ 和 $\mathcal{C}_e$ 的凹性半径。在 Avkhadiev--Wirths 关于开角为 $\pi A$（$A \in (1,2]$）的无界凸补集的共形映射的几何框架下，这些半径由显式超越方程刻画。通过构造与圆盘自同构 $\omega_0(z) = -z$ 相关的显式单叶极值函数，全局建立了尖锐性，并数值验证了这些半径关于参数 $A$ 的严格单调性。
英文摘要
We determine the radii of concavity for the classes $\mathcal{S}_e^*$ and $\mathcal{C}_e$ of univalent functions associated with the exponential mapping $e^z$. Under the geometric framework of Avkhadiev--Wirths for conformal mappings with unbounded convex complements of opening angle $πA$ ($A \in (1,2]$), the radii are characterized by explicit transcendental equations. Sharpness is established globally by constructing explicit univalent extremal functions related to the disk automorphism $ω_0(z) = -z$, and the strict monotonicity of these radii with respect to the parameter $A$ is verified numerically.
