Stable norms of non-orientable surfaces

Details Stable norms of non-orientable surfaces Stable norms of non-orientable surfaces

2007-03-22

arxiv.org/abs/math/0703667v1

Mathematics

Differential Geometry

Scientific paper

We study the stable norm on the first homology of a closed, non-orientable
surface equipped with a Riemannian metric. We prove that in every conformal
class there exists a metric whose stable norm is polyhedral. Furthermore the
stable norm is never strictly convex if the first Betti number of the surface
is greater than two.

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