Quasi-Fuchsian manifolds with particles

Abstract

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than $\pi$: any first-order deformation changes either one of those angles or the conformal structure at infinity, with marked points corresponding to the endpoints of the singular lines. Moreover, any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone-manifold structure.

Now 48 pages, no figure. v2: new title, various corrections, results extended to include graph singularities ("interacting particles"). v3: various corrections/improvements, in particular thanks to comments by an anonymous referee

References in corpus (1)

• On the renormalized volume of hyperbolic 3-manifolds

Cited by in corpus (2)

• On the renormalized volume of hyperbolic 3-manifolds
• Gauss images of hyperbolic cusps with convex polyhedral boundary