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2014 The convex core of quasifuchsian manifolds with particles
Cyril Lecuire, Jean-Marc Schlenker
Geom. Topol. 18(4): 2309-2373 (2014). DOI: 10.2140/gt.2014.18.2309


We consider quasifuchsian manifolds with “particles”, ie cone singularities of fixed angle less than π going from one connected component of the boundary at infinity to the other. Each connected component of the boundary at infinity is then endowed with a conformal structure marked by the endpoints of the particles. We prove that this defines a homeomorphism between the space of quasifuchsian metrics with n particles (of fixed angle) and the product of two copies of the Teichmüller space of a surface with n marked points. This extends the Bers double uniformization theorem to quasifuchsian manifolds with “particles”.

Quasifuchsian manifolds with particles also have a convex core. Its boundary has a hyperbolic induced metric, with cone singularities at the intersection with the particles, and is pleated along a measured geodesic lamination. We prove that any two hyperbolic metrics with cone singularities (of prescribed angle) can be obtained, and also that any two measured bending laminations, satisfying some obviously necessary conditions, can be obtained, as in Bonahon and Otal [Ann. of Math. 160 (2004) 1013–1055] in the nonsingular case.


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Cyril Lecuire. Jean-Marc Schlenker. "The convex core of quasifuchsian manifolds with particles." Geom. Topol. 18 (4) 2309 - 2373, 2014.


Received: 18 February 2013; Accepted: 5 October 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1334.57015
MathSciNet: MR3268778
Digital Object Identifier: 10.2140/gt.2014.18.2309

Primary: 20H10, 57M50

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.18 • No. 4 • 2014
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