no. 5
McShane-type identities for affine deformations
[Identités de type McShane pour déformations affines]
Charette, Virginie1 ; Goldman, William M.2
1 Département de mathématiques Université de Sherbrooke Sherbrooke, Québec J1K 2R1 (Canada)
2 Department of Mathematics University of Maryland College Park, MD 20742 (USA)
Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 2029-2041.

À partir des identités de McShane, de Mirzakhani et de Tan–Wong–Zhang, nous obtenons une identité pour les invariants de Margulis associés à une déformation affine d’une surface hyperbolique complète, orientable, à un trou. Il en découle le corollaire suivant : une déformation de la surface, dont les courbes simples fermées intérieures s’allongent infinitésimalement, doit également allonger le bord de manière infinitésimale.

We derive an identity for Margulis invariants of affine deformations of a complete orientable one-ended hyperbolic surface following the identities of McShane, Mirzakhani and Tan–Wong–Zhang. As a corollary, a deformation of the surface which infinitesimally lengthens all interior simple closed curves must infinitesimally lengthen the boundary.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3128
Classification : 57M05, 53C50
Keywords: hyperbolic surface, Margulis spacetime, closed geodesic, McShane identity
Mot clés : surface hyperbolique, espace-temps de Margulis, géodésique fermée, identité de McShane
Charette, Virginie 1 ; Goldman, William M. 2

1 Département de mathématiques Université de Sherbrooke Sherbrooke, Québec J1K 2R1 (Canada)
2 Department of Mathematics University of Maryland College Park, MD 20742 (USA) 
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Charette, Virginie; Goldman, William M. McShane-type identities for affine deformations. Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 2029-2041. doi : 10.5802/aif.3128. http://archive.numdam.org/articles/10.5802/aif.3128/

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