Laminations mesurées de plissage des variétés hyperboliques de dimension 3

Bonahon, Francis; Otal, Jean-Pierre

doi:10.4007/annals.2004.160.1013

Cited by 63 publications

(133 citation statements)

References 17 publications

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“…Theorem is 1.7 less general than the main result of [Sch02] insofar as the circle patterns considered are strictly hyperideal rather than hyperideal (a more general notion), but also more general since M can have compressible boundary and ∂M is allowed to have toric components. The proof of Theorem 1.7, however, is completely different from the one given in [Sch02]; here we show that Theorem 1.7 is a direct consequence of a result of Otal [Ota94,BO01], which itself uses crucially a result of Hodgson and Kerckhoff [HK98]. In [Sch02], the proof is direct and based, among other things, on some properties of the volume of hyperideal polyhedra.…”

Section: Some Examplesmentioning

confidence: 72%

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Hyperideal circle patterns

Schlenker¹

2005

Mathematical Research Letters

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Abstract. A "hyperideal circle pattern" in S 2 is a finite family of oriented circles, similar to an "usual" circle pattern but such that the closed disks bounded by the circles do not cover the whole sphere. Hyperideal circle patterns are directly related to hyperideal hyperbolic polyhedra, and also to circle packings.To each hyperideal circle pattern, one can associate an incidence graph and a set of intersection angles. We characterize the possible incidence graphs and intersection angles of hyperideal circle patterns in the sphere, the torus, and in higher genus surfaces. It is a consequence of a more general result, describing the hyperideal circle patterns in the boundaries of geometrically finite hyperbolic 3-manifolds (for the corresponding CP 1 -structures). This more general statement is obtained as a consequence of a theorem of Otal [Ota94, BO01] on the pleating laminations of the convex cores of geometrically finite hyperbolic manifolds.Résumé Un "motif de cercles hyperidéal" sur S 2 est une famille finie de cercles orientés, similaireà un motif de cercles "usuel" mais tel que la réunion des disques fermés bordés par les cercles ne couvre pas la sphère. Les motifs de cercles hyperidéaux sont directement liés aux polyèdres hyperboliques hyperidéaux, et aussi aux empilements de cercles.A chaque motif de cercles hyperidéal, on associe un graphe d'incidence et un ensemble d'angles d'intersection. On caractérise les graphes d'incidence et les angles d'intersection possibles dans la sphère, le tore, et sur les surfaces de genre supérieur. C'est une conséquence d'un résultat plus général décrivant les motifs de cercles hyperidéaux dans les bords de variétés hyperboliques géométriquement finies (pour les CP 1 -structures correspondantes). Ce résultat plus général est obtenu comme conséquence d'un théorème d'Otal [Ota94, BO01] sur les laminations de plissage des coeurs convexes de variétés hyperboliques géométriquement finies.

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Section: Some Examplesmentioning

confidence: 72%

“…Theorem 3.1 (Otal [Ota94,BO01]). Let N be a compact 3-manifold with boundary, whose interior admits a complete hyperbolic metric.…”

Section: A Theorem Of Otalmentioning

confidence: 99%

Hyperideal circle patterns

Schlenker¹

2005

Mathematical Research Letters

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“…As for prescribing the bending lamination, still in the hyperbolic setting, the existence has been proved recently by Bonahon and Otal [33] for convex co-compact manifolds with incompressible boundary (and, for general convex co-compact manifolds, by Lecuire [76]). However, for prescribing either the induced metric or the bending lamination, the uniqueness remains unknown, basically because we do not know whether infinitesimal rigidity holds, i.e.…”

Section: N7 Anti-de Sitter Manifoldsmentioning

confidence: 99%

Notes on a paper of Mess

et al. 2007

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“…The left-hand side of Figure 6 shows an example of the disks of type + with the simply connected union failing to satisfy conditions (3) and (4). The right-hand side of Figure 6 shows the disks of type + satisfying condition (4). As it can be seen, this does not prevent the disks that are not connected by edges to intersect each other.…”

Section: Projective Complexes Of Disksmentioning

confidence: 90%