The bending map of a hyperbolic -manifold maps a convex cocompact hyperbolic metric on a -manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.
L’application de plissage d’une variété hyperbolique de dimension associe à une métrique hyperbolique convexe cocompacte sur une variété compacte à bord sa lamination géodésique mesurée de plissage. Il a été démontré dans [KeS] et [KaT] que cette application est continue. Dans ce texte, on étudie l’extension de cette application à l’espace des métriques hyperboliques géométriquement finies. On introduit une relation d’équivalence dans l’espace des laminations géodésiques mesurées et on montre que l’application quotient de l’application de plissage est continue.
@article{AFST_2008_6_17_1_93_0,
author = {Cyril Lecuire},
title = {Continuity of the bending map},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {93--119},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 17},
number = {1},
year = {2008},
doi = {10.5802/afst.1178},
mrnumber = {2464096},
zbl = {1158.53027},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1178/}
}
TY - JOUR AU - Cyril Lecuire TI - Continuity of the bending map JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2008 SP - 93 EP - 119 VL - 17 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1178/ DO - 10.5802/afst.1178 LA - en ID - AFST_2008_6_17_1_93_0 ER -
%0 Journal Article %A Cyril Lecuire %T Continuity of the bending map %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2008 %P 93-119 %V 17 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1178/ %R 10.5802/afst.1178 %G en %F AFST_2008_6_17_1_93_0
Cyril Lecuire. Continuity of the bending map. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 93-119. doi : 10.5802/afst.1178. https://afst.centre-mersenne.org/articles/10.5802/afst.1178/
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