An integral representation formula of the Schwarzian derivative (Q1848422)

Let \(f\) be a conformal map of the unit disk onto a domain bounded by a curve \(C\), which is of class \(C^{3,\delta}\), except for a finite number of corners. Under a restriction on the angles at the corners, the authors derive a formula for the Schwarzian derivative of \(f\). The formula contains an integral of the arclength derivative of the curvature of \(C\) and a sum of polar terms corresponding to the corners.