- Date de réalisation : 28 Juin 2016
- Durée du programme : 61 min
- Classification Dewey : Mathématiques
Dans la même collectionT. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds R. Perales - Recent Intrinsic Flat Convergence Theorems R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions A. Mondino - Time-like Ricci curvature bounds via optimal transport D. Semola - Boundary regularity and stability under lower Ricci bounds C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
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.