What is Riemann mapping theorem?
The '''Riemann mapping theorem''' says that for every region (without holes) on the [<nowiki/>[[complex plane]]], there exists a smooth, angle-preserving, one-to-one map that takes our region to the unit disk. (The unit disk is the inside of the circle of radius 1 centered at the origin). This map is uniquely determined if you pick a point in your starting region to map to the origin, such that the [[Derivative (mathematics)|derivative]] at that point is on the real line and strictly greater than zero. [[Category:Theorems in geometry]]