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We review and extend here some recent results on the existence of minimalsurfaces and isoperimetric sets in non homogeneous and anisotropic periodicmedia. We also describe the qualitative properties of the homogenized surfacetension, also known as stable norm (or minimal action) in Weak KAM theory. Inparticular we investigate its strict convexity and differentiabilityproperties.

Existence and qualitative properties of isoperimetric sets in periodic media