A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their   symmetries
  For an embedded singly periodic minimal surface M with genus bigger than or equal to 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces. 
Valerio Ramos-Batista, Plinio Simoes