Koebe quarter theorem

The Koebe quarter theorem is a concept from complex analysis that concerns functions mapping a small, circular region in the complex plane onto other shapes. It states that if such a function is conformal (angle-preserving) and normalized in a specific way, then the image of a quarter of the original circle always contains a disk with a certain minimum size. In essence, it guarantees that these mappings are "large enough" in a precise sense, ensuring that the transformed region doesn't become too tiny or distorted, which helps mathematicians understand how these functions behave in a predictable and controlled manner.