Reference : Volumes of quasifuchsian manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/39407
Volumes of quasifuchsian manifolds
English
Schlenker, Jean-Marc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > >]
Mar-2020
Journal of Differential Geometry
International Press
Surveys in Differential Geometry, vol 23
Yes
International
0022-040X
1945-743X
Bethlehem
PA
[en] Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the volume, or more precisely the ``dual volume'', of the convex core. On one hand, there are striking similarities between them, for instance in their variational formulas. On the other, object related to them tend to be within bounded distance. Those analogies and proximities lead to several questions. Both the renormalized volume and the dual volume can be used for instance to bound the volume of the convex core in terms of the Weil-Petersson distance between the conformal metrics at infinity.
http://hdl.handle.net/10993/39407

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