Minimal surfaces with micro-oscillations
  We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of minimal graphs that are almost flat but have small oscillations whose geometry we can control. 
Alberto Enciso, M. Angeles Garcia-Ferrero and Daniel Peralta-Salas
math.DG math.AP