DIFFERENTIABILITY OF THE STABLE NORM IN CODIMENSION ONE

@inproceedings{Auer2006DIFFERENTIABILITYOT,
  title={DIFFERENTIABILITY OF THE STABLE NORM IN CODIMENSION ONE},
  author={Franz Auer and Victor Bangert},
  year={2006}
}
The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on Hn−1(M, R) is a homogenized version of the Riemannian (n−1)-volume. We study the differentiability properties of the stable norm at points α ∈ Hn−1(M, R). They depend on the position of α with respect to the integer lattice Hn−1(M, Z) in Hn−1(M, R). In… CONTINUE READING

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