On the renormalized volume of hyperbolic 3-manifolds
| dc.creator | Krasnov, Kirill | |
| dc.creator | Schlenker, Jean-Marc | |
| dc.date | 2006-07-04 | |
| dc.date | 2006-12-19 | |
| dc.date.accessioned | 2026-07-07T11:28:13Z | |
| dc.date.available | 2026-07-07T11:28:13Z | |
| dc.description | The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main aim of the present paper is to elucidate its geometrical meaning. We use another regularization procedure based on surfaces equidistant to a given convex surface \partial N. The renormalized volume computed via this procedure is equal to what we call the W-volume of the convex region N given by the usual volume of N minus the quarter of the integral of the mean curvature over \partial N. The W-volume satisfies some remarkable properties. First, this quantity is self-dual in the sense explained in the paper. Second, it verifies some simple variational formulas analogous to the classical geometrical Schlafli identities. These variational formulas are invariant under a certain transformation that replaces the data at \partial N by those at infinity of M. We use the variational formulas in terms of the data at infinity to give a simple geometrical proof of results of Takhtajan et al on the Kahler potential on various moduli spaces. | |
| dc.description | 23 pages, no figures (v2): proofs simplified, references added (v3): minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0607081 | |
| dc.identifier | http://arxiv.org/abs/math/0607081 | |
| dc.identifier | Commun.Math.Phys.279:637-668,2008 | |
| dc.identifier | doi:10.1007/s00220-008-0423-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/196373 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | On the renormalized volume of hyperbolic 3-manifolds | |
| dc.type | text |