Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces
| dc.creator | Fillastre, François | |
| dc.date | 2006-05-15 | |
| dc.date | 2006-08-31 | |
| dc.date.accessioned | 2026-07-07T07:52:19Z | |
| dc.date.available | 2026-07-07T07:52:19Z | |
| dc.description | A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly one convex Fuchsian polyhedron (up to global isometries). This extends a famous theorem of A.D. Alexandrov. | |
| dc.description | Some little corrections from the preceding version. To appear in Les Annales de l'Institut Fourier | |
| dc.identifier | https://arxiv.org/abs/math/0605403 | |
| dc.identifier | http://arxiv.org/abs/math/0605403 | |
| dc.identifier | Ann. Inst. Fourier (Grenoble) 57 (03/2007) 163--195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125838 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C45, 52A55, 52B70,53C24 | |
| dc.title | Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces | |
| dc.type | text |