Calculus of Variations and Geometric Measure Theory

A. Chambolle - M. Goldman - M. Novaga

Plane-like minimizers and differentiability of the stable norm

created by goldman on 07 May 2012
modified by novaga on 17 Apr 2016


Published Paper

Inserted: 7 may 2012
Last Updated: 17 apr 2016

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


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