Fuchsian polyhedra in Lorentzian space-forms
| dc.creator | Fillastre, François | |
| dc.date | 2007-02-18 | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:15Z | |
| dc.date.available | 2026-07-07T12:47:15Z | |
| dc.description | Let S be a compact surface of genus >1, and g be a metric on S of constant curvature K\in\{-1,0,1\} with conical singularities of negative singular curvature. When K=1 we add the condition that the lengths of the contractible geodesics are >2π. We prove that there exists a convex polyhedral surface P in the Lorentzian space-form of curvature K and a group G of isometries of this space such that the induced metric on the quotient P/G is isometric to (S,g). Moreover, the pair (P,G) is unique (up to global isometries) among a particular class of convex polyhedra, namely Fuchsian polyhedra. This extends theorems of A.D. Alexandrov and Rivin--Hodgson concerning the sphere to the higher genus cases, and it is also the polyhedral version of a theorem of Labourie--Schlenker. | |
| dc.identifier | https://arxiv.org/abs/math/0702532 | |
| dc.identifier | http://arxiv.org/abs/math/0702532 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221656 | |
| dc.subject | Differential Geometry | |
| dc.subject | 52B70 (Primary) 52A15,53C24,53C45 (Secondary) | |
| dc.title | Fuchsian polyhedra in Lorentzian space-forms | |
| dc.type | text |