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.
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.
Revised : 2016-08-02
Accepted : 2016-12-16
Published online : 2017-11-17
DOI : https://doi.org/10.5802/aif.3130
Classification: 57M50, 30F40, 30F45
Keywords: convex cocompact, hyperbolic 3-manifold, Renormalized Volume, Convex cores
@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},
publisher = {Association des Annales de l'institut Fourier},
volume = {67},
number = {5},
year = {2017},
pages = {2083-2098},
doi = {10.5802/aif.3130},
language = {en},
url = {http://www.numdam.org/item/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, Volume 67 (2017) no. 5, pp. 2083-2098. doi : 10.5802/aif.3130. http://www.numdam.org/item/AIF_2017__67_5_2083_0/
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