Hyperbolic manifolds with polyhedral boundary
| dc.creator | Schlenker, Jean-Marc | |
| dc.date | 2001-11-12 | |
| dc.date | 2002-09-30 | |
| dc.date.accessioned | 2026-07-07T04:44:33Z | |
| dc.date.available | 2026-07-07T04:44:33Z | |
| dc.description | Let $(M, \partial M)$ be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric $g$ on $M$ such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$ has curvature $K>-1$, and each such metric on $\dr M$ is obtained for a unique choice of $g$. A dual statement is that, for each $g$ as above, the third fundamental form of $\dr M$ has curvature $K<1$, and its closed geodesics which are contractible in $M$ have length $L>2π$. Conversely, any such metric on $\dr M$ is obtained for a unique choice of $g$. We are interested here in the similar situation where $\partial M$ is not smooth, but rather looks locally like an ideal polyhedron in $H^3$. We can give a fairly complete answer to the question on the third fundamental form -- which in this case concerns the dihedral angles -- and some partial results about the induced metric. This has some by-products, like an affine piecewise flat structure on the Teichmueller space of a surface with some marked points, or an extension of the Koebe circle packing theorem to many 3-manifolds with boundary. | |
| dc.description | Updated version on http://picard.ups-tlse.fr/~schlenker/texts/papers.html New version: several typos corrected, a few remarks added | |
| dc.identifier | https://arxiv.org/abs/math/0111136 | |
| dc.identifier | http://arxiv.org/abs/math/0111136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62630 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C45 | |
| dc.title | Hyperbolic manifolds with polyhedral boundary | |
| dc.type | text |