[Volume renormalisé et volume du cœur convexe]
On obtient des majorations et des minorations pour la différence entre le volume renormalisé et le volume du cœur convexe d’une variété hyperbolique convexe cocompacte qui dépendent du rayon d’injectivité du bord du revêtement universel du cœur convexe et de la caractéristique d’Euler du bord. Ces résultats généralisent ceux de Schlenker obtenus pour les 3-variétés quasifuchsiennes.
We obtain upper and lower bounds on the difference between the renormalized volume and the volume of the convex core of a convex cocompact hyperbolic 3-manifold which depend on the injectivity radius of the boundary of the universal cover of the convex core and the Euler characteristic of the boundary of the convex core. These results generalize results of Schlenker obtained in the setting of quasifuchsian hyperbolic 3-manifolds.
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Keywords: convex cocompact, hyperbolic 3-manifold, Renormalized Volume, Convex cores
Mot clés : convexe cocompact, 3-variétés hyperboliques, Volume renormalisé, cœurs convexes
@article{AIF_2017__67_5_2083_0,
author = {Bridgeman, Martin and Canary, Richard D.},
title = {Renormalized volume and the volume of the convex core},
journal = {Annales de l'Institut Fourier},
pages = {2083--2098},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {67},
number = {5},
year = {2017},
doi = {10.5802/aif.3130},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.3130/}
}
TY - JOUR AU - Bridgeman, Martin AU - Canary, Richard D. TI - Renormalized volume and the volume of the convex core JO - Annales de l'Institut Fourier PY - 2017 SP - 2083 EP - 2098 VL - 67 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3130/ DO - 10.5802/aif.3130 LA - en ID - AIF_2017__67_5_2083_0 ER -
%0 Journal Article %A Bridgeman, Martin %A Canary, Richard D. %T Renormalized volume and the volume of the convex core %J Annales de l'Institut Fourier %D 2017 %P 2083-2098 %V 67 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3130/ %R 10.5802/aif.3130 %G en %F AIF_2017__67_5_2083_0
Bridgeman, Martin; Canary, Richard D. Renormalized volume and the volume of the convex core. Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 2083-2098. doi : 10.5802/aif.3130. http://archive.numdam.org/articles/10.5802/aif.3130/
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