acase@tulane.edu / We study the problem of computing the minimum homotopy area of a planar normal curve. The area of a homotopy is the area swept by the homotopy on the plane. First, we consider a specific class of curves, namely self-overlapping curves, and show that the minimum homotopy area of a self-overlapping curve is equal to its winding area. For an arbitrary normal curve, we show that there is a decomposition of the curve into the self-overlapping subcurves such that the minimum homotopy area can be computed as the sum of winding areas of each self-overlapping subcurve in the decomposition. / 1 / Karakoc, Selcuk