Mathematical Research Letters

Volume 20 (2013)

Number 4

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

Pages: 773 – 786

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n4.a12

Author

Jean-Marc Schlenker (Mathematics Research Unit, University of Luxembourg)

Abstract

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.

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