Volume-constrained minimizers for the prescribed curvature problem in   periodic media
  We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence after rescaling of the volume-constrained minimizers towards a suitable Wulff Shape, when the volume tends to infinity. 
Michael Goldman (CMAP), Matteo Novaga
math.AP math.DG math.OC