On the structure of the stable norm of periodic metrics

Abstract

We study the differentiability of the stable norm associated with a Z n periodic metric on R n . Extending one of the main results of [Ba2], we prove that if p R n and the coordinates of p are linearly independent over Q, then there is a linear 2-plane V containing p such that the restriction of to V is differentiable at p. We construct examples where it is not differentiable at a point with coordinates linearly independent over Q.