McShane-type identities for affine deformations
Annales de l'Institut Fourier, Volume 67 (2017) no. 5, p. 2029-2041

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.

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.

Received : 2015-07-17
Accepted : 2016-12-16
Published online : 2017-11-17
DOI : https://doi.org/10.5802/aif.3128
Classification:  57M05,  53C50
Keywords: hyperbolic surface, Margulis spacetime, closed geodesic, McShane identity
@article{AIF_2017__67_5_2029_0,
     author = {Charette, Virginie and Goldman, William M.},
     title = {McShane-type identities for affine deformations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {5},
     year = {2017},
     pages = {2029-2041},
     doi = {10.5802/aif.3128},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2017__67_5_2029_0}
}
Charette, Virginie; Goldman, William M. McShane-type identities for affine deformations. Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2029-2041. doi : 10.5802/aif.3128. http://www.numdam.org/item/AIF_2017__67_5_2029_0/

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