Stable norms of non-orientable surfaces  [ Normes stables des surfaces non-orientables ]
Annales de l'Institut Fourier, Tome 58 (2008) no. 4, pp. 1337-1369.

Nous étudions la norme stable sur le premier groupe d’homologie d’une surface fermée et non-orientable munie d’une métrique riemannienne. Nous montrons qu’il existe dans chaque classe conforme une métrique dont la norme stable est polyèdrale. De plus, la norme stable est strictement convexe dès que le premier nombre de Betti est au moins trois.

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.

DOI : https://doi.org/10.5802/aif.2386
Classification : 37J50,  53C20,  53C23
Mots clés : surface non-orientable, norme stable
@article{AIF_2008__58_4_1337_0,
     author = {Balacheff, Florent and Massart, Daniel},
     title = {Stable norms of non-orientable surfaces},
     journal = {Annales de l'Institut Fourier},
     pages = {1337--1369},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {4},
     year = {2008},
     doi = {10.5802/aif.2386},
     mrnumber = {2427962},
     zbl = {pre05303677},
     language = {en},
     url = {archive.numdam.org/item/AIF_2008__58_4_1337_0/}
}
Balacheff, Florent; Massart, Daniel. Stable norms of non-orientable surfaces. Annales de l'Institut Fourier, Tome 58 (2008) no. 4, pp. 1337-1369. doi : 10.5802/aif.2386. http://archive.numdam.org/item/AIF_2008__58_4_1337_0/

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