Inserted: 24 jan 2011
Last Updated: 15 mar 2013
Journal: Calc. Var. and PDE
In this version the statement of Lemma 2.5 has been corrected with respect to the published version.
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.