Article (Scientific journals)
Volumes of quasifuchsian manifolds
Schlenker, Jean-Marc
2020In Surveys in Differential Geometry, 25 (1), p. 319-353
Peer reviewed
 

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Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Schlenker, Jean-Marc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC)
External co-authors :
no
Language :
English
Title :
Volumes of quasifuchsian manifolds
Publication date :
2020
Journal title :
Surveys in Differential Geometry
ISSN :
1052-9233
eISSN :
2164-4713
Publisher :
International Press, Cambridge, United States
Volume :
25
Issue :
1
Pages :
319-353
Peer reviewed :
Peer reviewed
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since 28 April 2019

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