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.
|Original language||English (US)|
|Number of pages||18|
|Journal||Mathematical Research Letters|
|State||Published - 1997|
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