We provide geometric estimates for conformal maps of the unit disc. As a consequence, a bound for the derivative of such maps follows yielding, in particular, an answer to a question posed by Martín Chuaqui. Finally, estimates regarding the curvature of image arcs under conformal maps are also obtained.

中文翻译：

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关于单价函数的几何估计

我们为单位圆盘的保形图提供了几何估计。结果，跟随这些图的导数的边界产生了，尤其是对马丁·丘基（MartínChuaqui）提出的问题的答案。最后，还获得了关于在保角图下图像弧度曲率的估计。