On the structure of the stable norm of periodic metrics

D. Burago, S. Ivanov, B. Kleiner

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)791-808
Number of pages18
JournalMathematical Research Letters
Issue number6
StatePublished - 1997

ASJC Scopus subject areas

  • General Mathematics


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