Stable norms of non-orientable surfaces
[Normes stables des surfaces non-orientables]
Balacheff, Florent1 ; Massart, Daniel2
1 Université de Neuchâtel Institut de mathématiques Rue Émile Argand 11 CP 158 2009 Neuchâtel (Switzerland)
2 Université Montpellier II Institut de Mathématiques et de Modélisation de Montpellier UMR 5149 Case Courier 051 Place Eugène Bataillon 34095 Montpellier Cedex 5 (France)
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 : 10.5802/aif.2386
Classification : 37J50, 53C20, 53C23
Keywords: Minimizing measures, non-orientable surface, stable norm
Mot clés : surface non-orientable, norme stable
Balacheff, Florent 1 ; Massart, Daniel 2

1 Université de Neuchâtel Institut de mathématiques Rue Émile Argand 11 CP 158 2009 Neuchâtel (Switzerland)
2 Université Montpellier II Institut de Mathématiques et de Modélisation de Montpellier UMR 5149 Case Courier 051 Place Eugène Bataillon 34095 Montpellier Cedex 5 (France) 
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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://www.numdam.org/articles/10.5802/aif.2386/

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