Published Paper

Inserted: 7 may 2012
Last Updated: 17 apr 2016

Journal: J. Geometric Analysis
Volume: 24
Number: 3
Pages: 1447-1489
Year: 2014

Abstract:

In this paper we investigate the strict convexity and the differentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly elliptic case). We prove that it is always differentiable in totally irrational directions, while in other directions, it is differentiable if and only if the corresponding plane-like minimizers satisfying a strong Birkhoff property foliate the torus. We also discuss the issue of the uniqueness of the correctors for the corresponding homogenization problem.

Keywords: minimal surfaces, plane-like minimizers, Geometric KAM theory

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