The renormalized volume and the volume of the convex core of quasifuchsian manifolds

Jean-Marc Schlenker (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We show that the renormalized volume of a quasifuchsian hyperbolic 3-manifold is equal, up to an additive constant, to the volume of its convex core. We also provide a precise upper bound on the renormalized volume in terms of the Weil-Petersson distance between the conformal structures at infinity. As a consequence we show that holomorphic disks in Teichmüller space which are large enough must have "enough" negative curvature.

Domaines: Géométrie différentielle [math.DG]; Topologie géométrique [math.GT]

Jean-Marc Schlenker. The renormalized volume and the volume of the convex core of quasifuchsian manifolds. 2011. ⟨hal-00636427⟩