THE MAPPING BY HEIGHTS FOR QUADRATIC-DIFFERENTIALS IN THE DISK

The heights of simple closed loops with respect to a holomorphic quadratic differential play an important role on compact Riemann surfaces. Here, the analogue is developed for quadratic differentials of finite norm in the disk. The height of a loop is replaced by the height of a cross cut, which is the same as the vertical distance, with respect to the q.d., of its end points.