[PDF][PDF] On the structure of the stable norm of periodic metrics
D Burago, S Ivanov, B Kleiner - Mathematical Research Letters, 1997 - Citeseer
D Burago, S Ivanov, B Kleiner
Mathematical Research Letters, 1997•CiteseerWe study the differentiability of the stable norm"." associated with a Zn periodic metric on Rn.
Extending one of the main results of [Ba2], we prove that if p∈ Rn 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.
Extending one of the main results of [Ba2], we prove that if p∈ Rn 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.
Abstract
We study the differentiability of the stable norm"." associated with a Zn periodic metric on Rn. Extending one of the main results of [Ba2], we prove that if p∈ Rn 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.
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