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Lengthening deformations of singular hyperbolic tori
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1239-1260.

Let S be a torus with a hyperbolic metric admitting one puncture or cone singularity. We describe which infinitesimal deformations of S lengthen (or shrink) all closed geodesics. We also study how the answer degenerates when S becomes Euclidean, i.e. very small.

Soit S un tore muni d’une métrique hyperbolique admettant un trou ou une singularité conique. Nous décrivons quelles déformations infinitésimales de S allongent (ou raccourcissent) toutes les géodésiques fermées. Nous étudions aussi comment la réponse à cette question dégénère lorsque S devient euclidienne, c’est-à-dire très petite.

DOI: 10.5802/afst.1483
François Guéritaud 1, 2

1 CNRS and Université Lille 1, Laboratoire Paul Painlevé, 59655 Villeneuve d’Ascq Cedex, France
2 Wolfgang-Pauli Institute, University of Vienna, CNRS-UMI 2842, Austria
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     title = {Lengthening deformations of singular hyperbolic tori},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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François Guéritaud. Lengthening deformations of singular hyperbolic tori. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1239-1260. doi : 10.5802/afst.1483. https://afst.centre-mersenne.org/articles/10.5802/afst.1483/

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