TY - JOUR

T1 - On the structure of the stable norm of periodic metrics

AU - Burago, Dmitri

AU - Ivanov, S.

AU - Kleiner, B.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031283708&partnerID=8YFLogxK

U2 - 10.4310/MRL.1997.v4.n6.a2

DO - 10.4310/MRL.1997.v4.n6.a2

M3 - Article

AN - SCOPUS:0031283708

VL - 4

SP - 791

EP - 808

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 6

ER -