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

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

2011-09-29

arxiv.org/abs/1109.6663v1

Mathematics

Differential Geometry

9 pages, no figure

Scientific paper

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 Teichm\"uller space which are large enough must have "enough" negative curvature.

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