Inserted: 7 nov 2012
Last Updated: 15 may 2016
Journal: in Geometric Partial Differential Equations, Edizioni della Normale, CRM Series
We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we investigate its strict convexity and differentiability properties.