Lower Segments of M-Curves

Convex M-Curves. The name M-Curve (Monotropic Curve) is due to Stackel. H. Mohrmann, in adopting the name, gives the following (precise definition : " A singularity-free (that which does not intersect itself) real branch of an analytic curve, which divides the Euclidean plane into two, and only two, regions, and for which the curvature at every finite point is limited and different from zero, will be called a limited monotropic curve or simply an M-Curve." (Mathetnatische Annalen, 72, 1912).