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Article overview
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The Weil-Petersson metric and the renormalized volume of hyperbolic 3-manifolds | | Kirill Krasnov
; Jean-Marc Schlenker
; | | Date: |
15 Jul 2009 | | Abstract: | We survey the renormalized volume of hyperbolic 3-manifolds, as a tool for
Teichmuller theory, using simple differential geometry arguments to recover
results sometimes first achieved by other means. One such application is
McMullen’s quasifuchsian (or more generally Kleinian) reciprocity, for which
different arguments are proposed. Another is the fact that the renormalized
volume of quasifuchsian (or more generally geometrically finite) hyperbolic
3-manifolds provides a Kahler potential for the Weil-Petersson metric on
Teichmuller space. Yet another is the fact that the grafting map is symplectic,
which is proved using a variant of the renormalized volume defined for
hyperbolic ends. | | Source: | arXiv, 0907.2590 | | Services: | Forum | Review | PDF | Favorites | |
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