Stable norms of non-orientable surfaces
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- March 2007
- DOI:
- arXiv:
- arXiv:math/0703667
- Bibcode:
- 2007math......3667B
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Dynamical Systems;
- 37J50;
- 53C20;
- 53C23
- E-Print:
- Annales de l'Institut Fourier, Vol. 58 (2008), No 4 , 1337-1369