Constant mean curvature surfaces of any positive genus
  We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends. 
S-P Kobayashi, M Kilian, W Rossman and N Schmitt