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Stable norms of non-orientable surfaces

Florent Balacheff·Daniel Massart
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Abstract

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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Florent Balacheff, Daniel Massart. 2007-03-22. Stable norms of non-orientable surfaces. https://arxiv.org/abs/math/0703667

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