- Date de réalisation : 28 Juin 2016
- Durée du programme : 61 min
- Classification Dewey : Mathématiques
Dans la même collectionX. Yuan - On the arithmetic degree of Shimura curves Ö. Yurttas - Algorithms for multicurves with Dynnikov coordinates A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 1) A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 3) P. Apisa - Marked points in genus two and beyond J. Aramayona - MCG and infinite MCG (Part 2)
Greg McShane - Volumes of hyperbolics manifolds and translation distances
Schlenker and Krasnov have established a remarkable Schlaffli-type formula for the (renormalized) volume of a quasi-Fuchsian manifold. Using this, some classical results in complex analysis and Gromov-Hausdorff convergence for sequences of open 3-manifolds due to Brock-Bromberg one obtains explicit upper bounds for the volume of a mapping torus in terms of the translation distance of the monodromy on Teichmueller space. We will explain Brock-Bromberg's approach to the Thurston's uniformization theorem for hyperbolic manifolds which are mapping tori. In particular the "coarse geometry" of the convex core of a quasi fuchsian manifold.