New constant mean curvature surfaces

We use the Dorfmeister-Pedit-Wu construction to present three new classes o f immersed CMC cylinders, each of which includes surfaces with umbilics. Th e first class consists of cylinders with one end asymptotic to a Delaunay s urface. The second class presents surfaces with a closed planar geodesic. I n the third class each surface has a closed curve of points With a Common t angent plane. An appendix, by the third author, describes the DPW potential s that appear to give CMC punctured spheres with k Delaunay ends (k-noids): the evidence is experimental at present. These can have both unduloidal an d nodoidal ends.