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The renormalized volume and the volume of the convex core of quasifuchsian manifolds
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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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Cited by 1 Pith paper
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Behaviour of the Schwarzian derivative on long complex projective tubes
On long complex projective tubes, the Schwarzian derivative is asymptotically (1/2z^2)(1+4π^2/ℓ^2) dz^2 up to exponentially small errors, giving control of renormalized volume under earthquakes and grafting.
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