Extending immersed circles in the sphere to immersed disks in the ball
J. Scott Carter · Commentarii Mathematici Helvetici · 1992
Consider a general position immersion of a circle into the 2-sphere. Suppose the immersion has an even number of double points. Then there is a proper immersion of the 2-disk that has the given curve as its boundary. Of all such extentions there is one with a minimum number of triple points. This minimum is obtained algorithmically in terms of a number that is associated to the double point set.