  We construct codimension 1 surfaces of any dimension that minimize a periodic
nonlocal perimeter functional among surfaces that are periodic, cylindrically
symmetric and decreasing.
  These surfaces may be seen as a nonlocal analogue of the classical Delaunay
surfaces (onduloids). For small volume, most of their mass tends to be
concentrated in a periodic array and the surfaces are close to a periodic array
of balls (in fact, we give explicit quantitative bounds on these facts).
