Let be a torus with a hyperbolic metric admitting one puncture or cone singularity. We describe which infinitesimal deformations of lengthen (or shrink) all closed geodesics. We also study how the answer degenerates when becomes Euclidean, i.e. very small.
Soit un tore muni d’une métrique hyperbolique admettant un trou ou une singularité conique. Nous décrivons quelles déformations infinitésimales de allongent (ou raccourcissent) toutes les géodésiques fermées. Nous étudions aussi comment la réponse à cette question dégénère lorsque devient euclidienne, c’est-à-dire très petite.
@article{AFST_2015_6_24_5_1239_0,
author = {Fran\c{c}ois Gu\'eritaud},
title = {Lengthening deformations of singular hyperbolic tori},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1239--1260},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 24},
number = {5},
year = {2015},
doi = {10.5802/afst.1483},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1483/}
}
TY - JOUR AU - François Guéritaud TI - Lengthening deformations of singular hyperbolic tori JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2015 SP - 1239 EP - 1260 VL - 24 IS - 5 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1483/ DO - 10.5802/afst.1483 LA - en ID - AFST_2015_6_24_5_1239_0 ER -
%0 Journal Article %A François Guéritaud %T Lengthening deformations of singular hyperbolic tori %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2015 %P 1239-1260 %V 24 %N 5 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1483/ %R 10.5802/afst.1483 %G en %F AFST_2015_6_24_5_1239_0
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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