Twist Deformation 



Singly periodic minimal surfaces with a distinguished vertical symmetry axes sometimes allow a twist deformation which twists the surface around the axes. The existence of such a deformation has been established for the singly periodic Scherk surface, the CallahanHoffmanMeeks surface, and the singly periodic helicoid (with a handle).  
Two fundamental pieces of a slightly twisted Scherk surface. The verical planar ends have become helicoidal.  
Twisting further lets the surface degenerate: Under a proper normalization, the limit surface becomes a helicoid. Is there singly periodic surface whose twist deformation has as a limit the singly periodic helicoid with a handle? 

Surprisingly, one can twist the Scherk surfaces beyond the limit parameter. However, the new surfaces are not embedded anymore: 