Differentiability of the stable norm in codimension one
Abstract
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 alpha in Hn-1(M,R). They depend on the position of alpha with respect to the integer lattice Hn-1(M,Z) in Hn-1(M,R). In particular, we show that the stable norm is differentiable at alpha if alpha is totally irrational.
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