On the renormalized volume of quasifuchsian manifolds
On the renormalized volume of quasifuchsian manifolds
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Jean-Marc Schlenker, Institut de math茅matiques de Toulouse
The renormalized volume of quasifuchsian hyperbolic 3-manifolds was originally introduced for physical reasons. Takhtajan and Zograf (and others) discovered that it provides a K盲hler potential for the Weil-Petersson metric on Teichm眉ller space. We will give an elementary, differential-geometric account of this result. It can be extended to quasifuchsian manifolds having cone singularities along infinite lines, yielding results on the Teichm眉ller space of hyperbolic metrics with cone singularities (of prescribed angles) on a closed surface. (Based on joint works with K. Krasnov, C. Lecuire, S. Moroianu.)